{"id":227060,"date":"2022-07-01T14:06:27","date_gmt":"2022-07-01T08:36:27","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=227060"},"modified":"2023-09-25T10:14:03","modified_gmt":"2023-09-25T04:44:03","slug":"wave-optics-from-rgpv-engineering-physics-notes","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/wave-optics-from-rgpv-engineering-physics-notes\/","title":{"rendered":"Wave Optics From RGPV Engineering Physics Notes"},"content":{"rendered":"<\/p>\n<style type=\"text\/css\">\n<!--\n\tp {margin: 0; padding: 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0;}\t.ft580{font-size:16px;font-family:Times;color:#000000;}\n\t.ft581{font-size:16px;font-family:Times;color:#000000;}\n\t.ft582{font-size:14px;font-family:Times;color:#000000;}\n\t.ft583{font-size:9px;font-family:Times;color:#000000;}\n\t.ft584{font-size:16px;line-height:25px;font-family:Times;color:#000000;}\n--><\/p>\n<p><!--\n\tp {margin: 0; padding: 0;}\t.ft590{font-size:16px;font-family:Times;color:#000000;}\n\t.ft591{font-size:14px;font-family:Times;color:#000000;}\n\t.ft592{font-size:16px;line-height:25px;font-family:Times;color:#000000;}\n-->\n<\/style>\n<div id=\"page25-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559025.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:455px;white-space:nowrap\" class=\"ft250\">1&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:443px;white-space:nowrap\" class=\"ft251\"><b>UNIT&nbsp;&ndash;&nbsp;2&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:85px;left:150px;white-space:nowrap\" class=\"ft251\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:110px;left:420px;white-space:nowrap\" class=\"ft251\"><b>WAVE&nbsp;OPTICS&nbsp;&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:150px;left:397px;white-space:nowrap\" class=\"ft251\"><b>Unit-02\/Lecture-01&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:189px;left:150px;white-space:nowrap\" class=\"ft252\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:222px;left:150px;white-space:nowrap\" class=\"ft251\"><b>FRESNEL&nbsp;BIPRISM:-&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:248px;left:150px;white-space:nowrap\" class=\"ft250\">Fresnel&rsquo;s&nbsp;biprism is&nbsp;made&nbsp;by&nbsp;joining&nbsp;two&nbsp;thin&nbsp;prisms&nbsp;at&nbsp;their base&nbsp;to&nbsp;create&nbsp;a&nbsp;single&nbsp;<\/p>\n<p style=\"position:absolute;top:270px;left:150px;white-space:nowrap\" class=\"ft250\">triangular shape.&nbsp;Light&nbsp;from single&nbsp;slit&nbsp;S forms&nbsp;spherical waves&nbsp;incident&nbsp;on&nbsp;the&nbsp;biprism.&nbsp;<\/p>\n<p style=\"position:absolute;top:292px;left:150px;white-space:nowrap\" class=\"ft250\">Light passing&nbsp;through the&nbsp;lower&nbsp;section is&nbsp;refracted up, while&nbsp;light going&nbsp;into&nbsp;the&nbsp;top&nbsp;<\/p>\n<p style=\"position:absolute;top:314px;left:150px;white-space:nowrap\" class=\"ft250\">section is&nbsp;refracted down, forming&nbsp;a&nbsp;region where&nbsp;the&nbsp;beams&nbsp;interfere.&nbsp;This&nbsp;creates&nbsp;two&nbsp;<\/p>\n<p style=\"position:absolute;top:336px;left:150px;white-space:nowrap\" class=\"ft250\">virtual sources<i>&nbsp;&nbsp;<\/i>S<\/p>\n<p style=\"position:absolute;top:344px;left:276px;white-space:nowrap\" class=\"ft254\">1<\/p>\n<p style=\"position:absolute;top:336px;left:282px;white-space:nowrap\" class=\"ft250\">&nbsp;&nbsp;and S<\/p>\n<p style=\"position:absolute;top:344px;left:333px;white-space:nowrap\" class=\"ft254\">2<\/p>\n<p style=\"position:absolute;top:336px;left:339px;white-space:nowrap\" class=\"ft250\">,&nbsp;with&nbsp;an&nbsp;apparent&nbsp;separation&nbsp;a.&nbsp;A biprism&nbsp;is&nbsp;essentially&nbsp;two&nbsp;<\/p>\n<p style=\"position:absolute;top:358px;left:150px;white-space:nowrap\" class=\"ft250\">prisms,&nbsp;each&nbsp;of&nbsp;very&nbsp;small refractive&nbsp;angle&nbsp;&alpha;&nbsp;placed&nbsp;base&nbsp;to&nbsp;base.&nbsp;In&nbsp;reality&nbsp;the&nbsp;biprism is&nbsp;<\/p>\n<p style=\"position:absolute;top:380px;left:150px;white-space:nowrap\" class=\"ft250\">constructed&nbsp;from&nbsp;a&nbsp;single&nbsp;plate&nbsp;of glass&nbsp;by&nbsp;suitable&nbsp;grinding&nbsp;and polishing&nbsp;it;&nbsp;the&nbsp;obtuse&nbsp;<\/p>\n<p style=\"position:absolute;top:402px;left:150px;white-space:nowrap\" class=\"ft250\">angle&nbsp;of the&nbsp;prism&nbsp;is&nbsp;only&nbsp;slightly&nbsp;less&nbsp;than 180&deg;&nbsp;and the&nbsp;other&nbsp;angles&nbsp;is&nbsp;of the&nbsp;order&nbsp;of&nbsp;30&rsquo;&nbsp;<\/p>\n<p style=\"position:absolute;top:424px;left:150px;white-space:nowrap\" class=\"ft250\">are&nbsp;equal.&nbsp;<\/p>\n<p style=\"position:absolute;top:445px;left:150px;white-space:nowrap\" class=\"ft255\"><b>&nbsp;<br \/>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:511px;left:719px;white-space:nowrap\" class=\"ft256\"><b>&nbsp;<br \/><\/b>&nbsp;<\/p>\n<p style=\"position:absolute;top:567px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:588px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:610px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:632px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:654px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:676px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:698px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:720px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:742px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:764px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:786px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:808px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:830px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:852px;left:719px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:874px;left:150px;white-space:nowrap\" class=\"ft250\">&nbsp;<\/p>\n<p style=\"position:absolute;top:896px;left:150px;white-space:nowrap\" class=\"ft250\">The&nbsp;Fresnel Biprism consists&nbsp;of&nbsp;two&nbsp;prisms&nbsp;joined&nbsp;together to&nbsp;form an&nbsp;isosceles&nbsp;triangle.&nbsp;<\/p>\n<p style=\"position:absolute;top:918px;left:150px;white-space:nowrap\" class=\"ft250\">Light from&nbsp;the&nbsp;slit hits&nbsp;the&nbsp;prism&nbsp;and is&nbsp;refracted through each half of the&nbsp;prism.&nbsp;This&nbsp;light&nbsp;<\/p>\n<p style=\"position:absolute;top:940px;left:150px;white-space:nowrap\" class=\"ft250\">then interferes&nbsp;with itself to&nbsp;produce&nbsp;an&nbsp;interference&nbsp;pattern.&nbsp;Due&nbsp;to&nbsp;the&nbsp;fact that point&nbsp;<\/p>\n<p style=\"position:absolute;top:962px;left:150px;white-space:nowrap\" class=\"ft250\">sources&nbsp;are&nbsp;idealizations&nbsp;this&nbsp;is&nbsp;never&nbsp;the&nbsp;case&nbsp;and unwanted diffraction effects&nbsp;can occur.&nbsp;<\/p>\n<p style=\"position:absolute;top:984px;left:150px;white-space:nowrap\" class=\"ft250\">The&nbsp;Fresnel&nbsp;biprism&nbsp;overcomes&nbsp;this&nbsp;by&nbsp;replacing&nbsp;the&nbsp;two&nbsp;point sources&nbsp;with &ldquo;virtual&nbsp;slits&rdquo;.&nbsp;<\/p>\n<p style=\"position:absolute;top:1006px;left:150px;white-space:nowrap\" class=\"ft250\">These&nbsp;slits&nbsp;are&nbsp;created&nbsp;virtually&nbsp;by&nbsp;where&nbsp;the&nbsp;light appears&nbsp;to&nbsp;come&nbsp;from&nbsp;after&nbsp;it is&nbsp;<\/p>\n<p style=\"position:absolute;top:1028px;left:150px;white-space:nowrap\" class=\"ft250\">refracted through the&nbsp;slit.&nbsp;These&nbsp;virtual&nbsp;slits&nbsp;do&nbsp;behave&nbsp;as&nbsp;point&nbsp;sources&nbsp;and thus&nbsp;no&nbsp;<\/p>\n<p style=\"position:absolute;top:1050px;left:150px;white-space:nowrap\" class=\"ft258\">unwanted effects&nbsp;occur.&nbsp;Thus, we&nbsp;get two&nbsp;coherent sources.&nbsp;<br \/>&nbsp;<br \/>&nbsp;<br \/>&nbsp;<\/p>\n<\/div>\n<div id=\"page26-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559026.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:455px;white-space:nowrap\" class=\"ft260\">2&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft260\">&nbsp;<\/p>\n<p style=\"position:absolute;top:52px;left:150px;white-space:nowrap\" class=\"ft262\">&nbsp;<br \/>&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:108px;left:150px;white-space:nowrap\" class=\"ft260\">Consider&nbsp;that S&nbsp;and S&nbsp;are&nbsp;two&nbsp;virtual&nbsp;sources&nbsp;and are&nbsp;separated&nbsp;by a&nbsp;distance d&nbsp;<\/p>\n<p style=\"position:absolute;top:130px;left:150px;white-space:nowrap\" class=\"ft263\">The&nbsp;condition for&nbsp;maximum&nbsp;at a&nbsp;point P&nbsp;is&nbsp;<br \/>S<\/p>\n<p style=\"position:absolute;top:164px;left:160px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:158px;left:166px;white-space:nowrap\" class=\"ft260\">P&nbsp;&#8211;&nbsp;S<\/p>\n<p style=\"position:absolute;top:164px;left:200px;white-space:nowrap\" class=\"ft261\">1<\/p>\n<p style=\"position:absolute;top:158px;left:206px;white-space:nowrap\" class=\"ft260\">P =&nbsp;n&nbsp;<\/p>\n<p style=\"position:absolute;top:151px;left:248px;white-space:nowrap\" class=\"ft260\">&lambda;&nbsp;&nbsp;where&nbsp;n=&nbsp;0,1,2&hellip;&hellip;.&nbsp;<\/p>\n<p style=\"position:absolute;top:178px;left:150px;white-space:nowrap\" class=\"ft262\">&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:525px;left:553px;white-space:nowrap\" class=\"ft260\">&nbsp;<\/p>\n<p style=\"position:absolute;top:542px;left:480px;white-space:nowrap\" class=\"ft260\">&nbsp;<\/p>\n<p style=\"position:absolute;top:562px;left:150px;white-space:nowrap\" class=\"ft262\">&nbsp;<br \/>&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:619px;left:150px;white-space:nowrap\" class=\"ft263\">The&nbsp;path difference&nbsp;between the&nbsp;ray&nbsp;at a&nbsp;point&nbsp;P&nbsp;is&nbsp;<br \/>(S<\/p>\n<p style=\"position:absolute;top:653px;left:166px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:646px;left:172px;white-space:nowrap\" class=\"ft260\">P)<\/p>\n<p style=\"position:absolute;top:642px;left:188px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:646px;left:194px;white-space:nowrap\" class=\"ft260\">&nbsp;&#8211;&nbsp;(S<\/p>\n<p style=\"position:absolute;top:653px;left:225px;white-space:nowrap\" class=\"ft261\">1<\/p>\n<p style=\"position:absolute;top:646px;left:231px;white-space:nowrap\" class=\"ft260\">P)<\/p>\n<p style=\"position:absolute;top:642px;left:247px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:646px;left:253px;white-space:nowrap\" class=\"ft260\">&nbsp;<\/p>\n<p style=\"position:absolute;top:667px;left:150px;white-space:nowrap\" class=\"ft262\">&nbsp;<br \/>=&nbsp;[ D<\/p>\n<p style=\"position:absolute;top:684px;left:188px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:688px;left:194px;white-space:nowrap\" class=\"ft260\">&nbsp;+ (x&nbsp;+&nbsp;d\/2)<\/p>\n<p style=\"position:absolute;top:684px;left:276px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:688px;left:282px;white-space:nowrap\" class=\"ft260\">&nbsp;]&nbsp;&#8211;&nbsp;[ D<\/p>\n<p style=\"position:absolute;top:684px;left:331px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:688px;left:337px;white-space:nowrap\" class=\"ft260\">&nbsp;+ (x<\/p>\n<p style=\"position:absolute;top:694px;left:371px;white-space:nowrap\" class=\"ft261\">&nbsp;<\/p>\n<p style=\"position:absolute;top:688px;left:374px;white-space:nowrap\" class=\"ft260\">&#8211;&nbsp;d\/2)<\/p>\n<p style=\"position:absolute;top:684px;left:414px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:688px;left:420px;white-space:nowrap\" class=\"ft260\">&nbsp;]&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:708px;left:150px;white-space:nowrap\" class=\"ft262\">=&nbsp;2&nbsp;x&nbsp;d&hellip;&hellip;&hellip;(1)&nbsp;<br \/>Since S<\/p>\n<p style=\"position:absolute;top:735px;left:204px;white-space:nowrap\" class=\"ft261\">1&nbsp;<\/p>\n<p style=\"position:absolute;top:729px;left:213px;white-space:nowrap\" class=\"ft260\">S<\/p>\n<p style=\"position:absolute;top:735px;left:223px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:729px;left:229px;white-space:nowrap\" class=\"ft260\">&nbsp;=&nbsp;d and OP&nbsp;=&nbsp;x<\/p>\n<p style=\"position:absolute;top:735px;left:343px;white-space:nowrap\" class=\"ft261\">&nbsp;<\/p>\n<p style=\"position:absolute;top:729px;left:346px;white-space:nowrap\" class=\"ft260\">,&nbsp;we can&nbsp;write.&nbsp;<\/p>\n<p style=\"position:absolute;top:750px;left:150px;white-space:nowrap\" class=\"ft260\">S<\/p>\n<p style=\"position:absolute;top:756px;left:160px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:750px;left:166px;white-space:nowrap\" class=\"ft260\">P&nbsp;&#8211;&nbsp;S<\/p>\n<p style=\"position:absolute;top:756px;left:200px;white-space:nowrap\" class=\"ft261\">1<\/p>\n<p style=\"position:absolute;top:750px;left:206px;white-space:nowrap\" class=\"ft260\">P&nbsp;=&nbsp;2&nbsp;x<\/p>\n<p style=\"position:absolute;top:756px;left:257px;white-space:nowrap\" class=\"ft261\">&nbsp;<\/p>\n<p style=\"position:absolute;top:750px;left:260px;white-space:nowrap\" class=\"ft260\">d&nbsp;\/ (S<\/p>\n<p style=\"position:absolute;top:756px;left:299px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:750px;left:305px;white-space:nowrap\" class=\"ft260\">P +&nbsp;S<\/p>\n<p style=\"position:absolute;top:756px;left:344px;white-space:nowrap\" class=\"ft261\">1<\/p>\n<p style=\"position:absolute;top:750px;left:350px;white-space:nowrap\" class=\"ft260\">P)&hellip;&hellip;&hellip;&hellip;(2)&nbsp;<\/p>\n<p style=\"position:absolute;top:771px;left:150px;white-space:nowrap\" class=\"ft262\">&nbsp;<br \/>If&nbsp;d&lt;&lt;D&nbsp;and S<\/p>\n<p style=\"position:absolute;top:798px;left:254px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:791px;left:260px;white-space:nowrap\" class=\"ft260\">P +&nbsp;S<\/p>\n<p style=\"position:absolute;top:798px;left:298px;white-space:nowrap\" class=\"ft261\">1<\/p>\n<p style=\"position:absolute;top:791px;left:304px;white-space:nowrap\" class=\"ft260\">P =&nbsp;2D&nbsp;<\/p>\n<p style=\"position:absolute;top:812px;left:150px;white-space:nowrap\" class=\"ft262\">&nbsp;<br \/>Then&nbsp;we can&nbsp;write&nbsp;<br \/>&nbsp;<br \/>S<\/p>\n<p style=\"position:absolute;top:880px;left:160px;white-space:nowrap\" class=\"ft261\">2<\/p>\n<p style=\"position:absolute;top:874px;left:166px;white-space:nowrap\" class=\"ft260\">P&nbsp;&#8211;&nbsp;S<\/p>\n<p style=\"position:absolute;top:880px;left:200px;white-space:nowrap\" class=\"ft261\">1<\/p>\n<p style=\"position:absolute;top:874px;left:206px;white-space:nowrap\" class=\"ft260\">P =&nbsp;x&nbsp;d\/D&nbsp;=&nbsp;n&nbsp;<\/p>\n<p style=\"position:absolute;top:868px;left:308px;white-space:nowrap\" class=\"ft260\">&lambda;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:889px;left:150px;white-space:nowrap\" class=\"ft263\">&nbsp;<br \/>Thus&nbsp;y<\/p>\n<p style=\"position:absolute;top:923px;left:199px;white-space:nowrap\" class=\"ft261\">n<\/p>\n<p style=\"position:absolute;top:917px;left:205px;white-space:nowrap\" class=\"ft260\">&nbsp;=&nbsp;nD&nbsp;<\/p>\n<p style=\"position:absolute;top:910px;left:251px;white-space:nowrap\" class=\"ft260\">&lambda;&nbsp;\/ d&nbsp;<\/p>\n<p style=\"position:absolute;top:937px;left:150px;white-space:nowrap\" class=\"ft260\">&nbsp;<\/p>\n<p style=\"position:absolute;top:952px;left:150px;white-space:nowrap\" class=\"ft260\">The&nbsp;fringe&nbsp;width is&nbsp;the&nbsp;distance&nbsp;between two&nbsp;consecutive&nbsp;fringes&nbsp;<\/p>\n<p style=\"position:absolute;top:974px;left:150px;white-space:nowrap\" class=\"ft260\">&nbsp;<\/p>\n<p style=\"position:absolute;top:996px;left:150px;white-space:nowrap\" class=\"ft260\">&beta;&nbsp;=&nbsp;x<\/p>\n<p style=\"position:absolute;top:1008px;left:187px;white-space:nowrap\" class=\"ft261\">n+1<\/p>\n<p style=\"position:absolute;top:1002px;left:206px;white-space:nowrap\" class=\"ft260\">&nbsp;&ndash;&nbsp;x<\/p>\n<p style=\"position:absolute;top:1008px;left:233px;white-space:nowrap\" class=\"ft261\">n<\/p>\n<p style=\"position:absolute;top:1002px;left:239px;white-space:nowrap\" class=\"ft260\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1023px;left:150px;white-space:nowrap\" class=\"ft260\">&nbsp; &nbsp;&nbsp;=&nbsp;<\/p>\n<p style=\"position:absolute;top:1016px;left:183px;white-space:nowrap\" class=\"ft260\">&lambda;&nbsp;D\/d&nbsp;<\/p>\n<p style=\"position:absolute;top:1038px;left:142px;white-space:nowrap\" class=\"ft264\">&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:1104px;left:150px;white-space:nowrap\" class=\"ft260\">&nbsp;<\/p>\n<\/div>\n<div id=\"page27-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559027.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:455px;white-space:nowrap\" class=\"ft270\">3&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft274\">&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:86px;left:400px;white-space:nowrap\" class=\"ft271\"><b>Unit-02\/Lecture-02&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:125px;left:483px;white-space:nowrap\" class=\"ft270\">&nbsp;<\/p>\n<p style=\"position:absolute;top:147px;left:157px;white-space:nowrap\" class=\"ft271\"><b>EXPERIMENTAL DETERMINATION&nbsp;OF&nbsp;FRESNEL BIPRISM&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:173px;left:157px;white-space:nowrap\" class=\"ft270\">&nbsp;<\/p>\n<p style=\"position:absolute;top:195px;left:157px;white-space:nowrap\" class=\"ft272\"><b>APPARATUS:&nbsp;<\/b>Fresnel Biprism,&nbsp;convex&nbsp;lens,&nbsp;light&nbsp;source,&nbsp;measuring&nbsp;scale,&nbsp;microscope.&nbsp;<\/p>\n<p style=\"position:absolute;top:217px;left:157px;white-space:nowrap\" class=\"ft270\">&nbsp;<\/p>\n<p style=\"position:absolute;top:239px;left:157px;white-space:nowrap\" class=\"ft272\"><b>ADJUSTMENTS:&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:261px;left:157px;white-space:nowrap\" class=\"ft272\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:283px;left:157px;white-space:nowrap\" class=\"ft270\">Before&nbsp;carrying&nbsp;out the&nbsp;measurement of the&nbsp;fringe-width it is&nbsp;essential&nbsp;to&nbsp;obtain&nbsp;correct&nbsp;<\/p>\n<p style=\"position:absolute;top:305px;left:157px;white-space:nowrap\" class=\"ft270\">fringes&nbsp;in which the&nbsp;spacing&nbsp;is&nbsp;uniform&nbsp;on the&nbsp;entire&nbsp;field by&nbsp;carrying&nbsp;out the&nbsp;following&nbsp;<\/p>\n<p style=\"position:absolute;top:327px;left:157px;white-space:nowrap\" class=\"ft270\">adjustments&nbsp;in the&nbsp;apparatus:&nbsp;<\/p>\n<p style=\"position:absolute;top:349px;left:157px;white-space:nowrap\" class=\"ft270\">&nbsp;<\/p>\n<p style=\"position:absolute;top:371px;left:157px;white-space:nowrap\" class=\"ft270\">1.&nbsp;The&nbsp;bed&nbsp;of the&nbsp;optical&nbsp;bench is&nbsp;first leveled with the&nbsp;help of&nbsp;a&nbsp;spirit&nbsp;level&nbsp;and leveling&nbsp;<\/p>\n<p style=\"position:absolute;top:393px;left:157px;white-space:nowrap\" class=\"ft270\">screws.&nbsp;<\/p>\n<p style=\"position:absolute;top:415px;left:157px;white-space:nowrap\" class=\"ft270\">&nbsp;<\/p>\n<p style=\"position:absolute;top:437px;left:157px;white-space:nowrap\" class=\"ft270\">2.&nbsp;The&nbsp;eyepiece&nbsp;is&nbsp;focused on the&nbsp;cross&nbsp;wires&nbsp;by&nbsp;moving&nbsp;the&nbsp;tube&nbsp;containing&nbsp;the&nbsp;lenses&nbsp;in&nbsp;<\/p>\n<p style=\"position:absolute;top:459px;left:157px;white-space:nowrap\" class=\"ft270\">the&nbsp; &nbsp; &nbsp;crosswires&nbsp;tube&nbsp;until&nbsp;they&nbsp;are&nbsp;distinctly&nbsp;visible.&nbsp;One&nbsp;of the&nbsp;two&nbsp;wires&nbsp;in the&nbsp;cross&nbsp;<\/p>\n<p style=\"position:absolute;top:481px;left:157px;white-space:nowrap\" class=\"ft270\">wires&nbsp;is&nbsp;then&nbsp;made&nbsp;exactly&nbsp;vertical by&nbsp;observing&nbsp;a plumb&nbsp;line.&nbsp;<\/p>\n<p style=\"position:absolute;top:503px;left:157px;white-space:nowrap\" class=\"ft270\">&nbsp;<\/p>\n<p style=\"position:absolute;top:525px;left:157px;white-space:nowrap\" class=\"ft270\">3.&nbsp;The&nbsp;slit and the&nbsp;eyepiece&nbsp;are&nbsp;adjusted&nbsp;to&nbsp;the same height&nbsp;above the bench.Areal&nbsp;image&nbsp;<\/p>\n<p style=\"position:absolute;top:547px;left:157px;white-space:nowrap\" class=\"ft270\">of the&nbsp;illuminated slit is&nbsp;then formed&nbsp;in the&nbsp;plane&nbsp;of the&nbsp;crosswire&nbsp;by&nbsp;the&nbsp;help of a&nbsp;convex&nbsp;<\/p>\n<p style=\"position:absolute;top:569px;left:157px;white-space:nowrap\" class=\"ft270\">lens&nbsp;of small&nbsp;aperture.&nbsp;The&nbsp;slit is&nbsp;now rotated in its&nbsp;own plane&nbsp;by&nbsp;the&nbsp;help of a&nbsp;tangent&nbsp;<\/p>\n<p style=\"position:absolute;top:591px;left:157px;white-space:nowrap\" class=\"ft270\">screw&nbsp;until&nbsp;its&nbsp;image&nbsp;exactly&nbsp;coincides&nbsp;with the&nbsp;vertical&nbsp;wire&nbsp;in the&nbsp;eyepiece.&nbsp;The&nbsp;slit is&nbsp;<\/p>\n<p style=\"position:absolute;top:613px;left:157px;white-space:nowrap\" class=\"ft270\">then exactly&nbsp;vertical.&nbsp;<\/p>\n<p style=\"position:absolute;top:635px;left:157px;white-space:nowrap\" class=\"ft270\">&nbsp;<\/p>\n<p style=\"position:absolute;top:657px;left:157px;white-space:nowrap\" class=\"ft270\">4. The&nbsp;bi-prism is&nbsp;mounted,&nbsp;keeping&nbsp;its&nbsp;refracted&nbsp;edge&nbsp;nearly&nbsp;vertical,&nbsp;between&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:678px;left:157px;white-space:nowrap\" class=\"ft270\">eyepiece&nbsp;and the&nbsp;slit,&nbsp;which is&nbsp;made&nbsp;narrow and illuminated with the&nbsp;light&nbsp;whose&nbsp;<\/p>\n<p style=\"position:absolute;top:700px;left:157px;white-space:nowrap\" class=\"ft270\">wavelength is&nbsp;to&nbsp;be&nbsp;determined.&nbsp;<\/p>\n<p style=\"position:absolute;top:723px;left:157px;white-space:nowrap\" class=\"ft270\">5.&nbsp;The&nbsp;edge&nbsp;formed by&nbsp;the&nbsp;inter&nbsp;section of the&nbsp;inclined faces&nbsp;enclosing&nbsp;the&nbsp;obtuse&nbsp;angle&nbsp;<\/p>\n<p style=\"position:absolute;top:744px;left:157px;white-space:nowrap\" class=\"ft270\">in&nbsp;the&nbsp;biprism must&nbsp;be&nbsp;now&nbsp;adjusted&nbsp;exactly&nbsp;parallel to&nbsp;the&nbsp;vertical&nbsp;slit.&nbsp;To&nbsp;make&nbsp;this&nbsp;<\/p>\n<p style=\"position:absolute;top:766px;left:157px;white-space:nowrap\" class=\"ft270\">adjustment,&nbsp;two&nbsp;real images&nbsp;of the&nbsp;coherent sources&nbsp;S<\/p>\n<p style=\"position:absolute;top:775px;left:569px;white-space:nowrap\" class=\"ft273\">1<\/p>\n<p style=\"position:absolute;top:766px;left:575px;white-space:nowrap\" class=\"ft270\">&nbsp;and S<\/p>\n<p style=\"position:absolute;top:775px;left:623px;white-space:nowrap\" class=\"ft273\">2<\/p>\n<p style=\"position:absolute;top:766px;left:629px;white-space:nowrap\" class=\"ft270\">&nbsp;are&nbsp;formed&nbsp;in&nbsp;the&nbsp;focal&nbsp;<\/p>\n<p style=\"position:absolute;top:788px;left:157px;white-space:nowrap\" class=\"ft270\">plane&nbsp;of the&nbsp;eyepiece&nbsp;with the&nbsp;help of a&nbsp;convergent lens.&nbsp;By&nbsp;lateral&nbsp;movement of the&nbsp;<\/p>\n<p style=\"position:absolute;top:810px;left:157px;white-space:nowrap\" class=\"ft270\">prism,&nbsp;the&nbsp;images&nbsp;are&nbsp;made&nbsp;equally&nbsp;bright&nbsp;i.e.&nbsp;equally&nbsp;well&nbsp;focused&nbsp;and&nbsp;of&nbsp;equal height&nbsp;<\/p>\n<p style=\"position:absolute;top:832px;left:157px;white-space:nowrap\" class=\"ft270\">by&nbsp;rotation&nbsp;of the&nbsp;bi-prism&nbsp;in the&nbsp;vertical&nbsp;plane&nbsp;with the&nbsp;help of tangent screw.&nbsp;On&nbsp;<\/p>\n<p style=\"position:absolute;top:854px;left:157px;white-space:nowrap\" class=\"ft270\">removing&nbsp;the&nbsp;lens,&nbsp;this&nbsp;edge&nbsp;can&nbsp;be&nbsp;now&nbsp;made&nbsp;exactly&nbsp;parallel to&nbsp;the&nbsp;slit,&nbsp;by&nbsp;giving&nbsp;finer&nbsp;<\/p>\n<p style=\"position:absolute;top:876px;left:157px;white-space:nowrap\" class=\"ft270\">rotation to&nbsp;the&nbsp;prism.&nbsp;Until&nbsp;the&nbsp;interference&nbsp;fringes&nbsp;become&nbsp;perfectly&nbsp;distinct and well&nbsp;<\/p>\n<p style=\"position:absolute;top:898px;left:157px;white-space:nowrap\" class=\"ft270\">defined.&nbsp;<\/p>\n<p style=\"position:absolute;top:920px;left:157px;white-space:nowrap\" class=\"ft270\">&nbsp;<\/p>\n<p style=\"position:absolute;top:942px;left:157px;white-space:nowrap\" class=\"ft272\"><b>PROCEDURE:&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:964px;left:157px;white-space:nowrap\" class=\"ft272\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:986px;left:184px;white-space:nowrap\" class=\"ft270\">1.&nbsp;&nbsp;Focus&nbsp;the edge formed&nbsp;by the intersection&nbsp;of&nbsp;the inclined&nbsp;forces&nbsp;enclosing&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:1008px;left:211px;white-space:nowrap\" class=\"ft270\">obtuse&nbsp;angle&nbsp;in the&nbsp;bi-prism by&nbsp;making&nbsp;it&nbsp;parallel to&nbsp;the&nbsp;virtual slit.&nbsp;As&nbsp;in&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:1030px;left:211px;white-space:nowrap\" class=\"ft270\">displacement method of measuring&nbsp;the&nbsp;focal&nbsp;length, the&nbsp;lens&nbsp;is&nbsp;adjusted in&nbsp;a&nbsp;<\/p>\n<p style=\"position:absolute;top:1052px;left:211px;white-space:nowrap\" class=\"ft270\">position where&nbsp;magnified distinct and real&nbsp;images&nbsp;of the&nbsp;virtual&nbsp;coherent sources&nbsp;<\/p>\n<p style=\"position:absolute;top:1074px;left:211px;white-space:nowrap\" class=\"ft270\">are&nbsp;formed.&nbsp;The&nbsp;separation d1&nbsp;is&nbsp;then measured.&nbsp;The&nbsp;lens&nbsp;is&nbsp;now moved to&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:1096px;left:211px;white-space:nowrap\" class=\"ft270\">conjugate&nbsp;position, which forms&nbsp;distinct diminished images&nbsp;of the&nbsp;crosswire.&nbsp;<\/p>\n<p style=\"position:absolute;top:1118px;left:211px;white-space:nowrap\" class=\"ft270\">&nbsp;<\/p>\n<\/div>\n<div id=\"page28-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559028.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:455px;white-space:nowrap\" class=\"ft280\">4&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft280\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:184px;white-space:nowrap\" class=\"ft280\">2.&nbsp;&nbsp;Now remove&nbsp;this&nbsp;convex&nbsp;lens&nbsp;and&nbsp;&nbsp;move&nbsp;the&nbsp;eyepiece&nbsp;that distinct fringes&nbsp;are&nbsp;<\/p>\n<p style=\"position:absolute;top:68px;left:211px;white-space:nowrap\" class=\"ft280\">obtained.&nbsp;Measure&nbsp;the&nbsp;separation between say&nbsp;20&nbsp;fringes&nbsp;then calculate&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:90px;left:211px;white-space:nowrap\" class=\"ft280\">fringe&nbsp;width.&nbsp;<\/p>\n<p style=\"position:absolute;top:112px;left:211px;white-space:nowrap\" class=\"ft280\">&nbsp;<\/p>\n<p style=\"position:absolute;top:134px;left:157px;white-space:nowrap\" class=\"ft281\"><b>Measurement&nbsp;of&nbsp;the separation&nbsp;of&nbsp;two virtual&nbsp;sources&nbsp;(d):&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:156px;left:157px;white-space:nowrap\" class=\"ft281\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:178px;left:157px;white-space:nowrap\" class=\"ft280\">A&nbsp;convex&nbsp;lens&nbsp;is&nbsp;introduced between the&nbsp;bi-prism&nbsp;and the&nbsp;eyepiece&nbsp;and&nbsp;the&nbsp;latter&nbsp;is&nbsp;fixed&nbsp;<\/p>\n<p style=\"position:absolute;top:200px;left:157px;white-space:nowrap\" class=\"ft280\">at a&nbsp;distance&nbsp;from&nbsp;the&nbsp;slit which is&nbsp;greater&nbsp;than four&nbsp;times&nbsp;the&nbsp;focal&nbsp;length of the&nbsp;lens.&nbsp;As&nbsp;<\/p>\n<p style=\"position:absolute;top:222px;left:157px;white-space:nowrap\" class=\"ft280\">in displacement method of measuring&nbsp;the&nbsp;focal&nbsp;length, the&nbsp;lens&nbsp;is&nbsp;adjusted in a&nbsp;position&nbsp;<\/p>\n<p style=\"position:absolute;top:244px;left:157px;white-space:nowrap\" class=\"ft280\">marked,&nbsp;&nbsp;so&nbsp;that we&nbsp;get a&nbsp;magnified distinct&nbsp;real&nbsp;image&nbsp;of virtual&nbsp;sources&nbsp;on&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:266px;left:157px;white-space:nowrap\" class=\"ft280\">crosswire.&nbsp;By&nbsp;giving&nbsp;lateral&nbsp;displacement to&nbsp;the&nbsp;cross&nbsp;wires, the&nbsp;separation d<\/p>\n<p style=\"position:absolute;top:274px;left:782px;white-space:nowrap\" class=\"ft282\">1<\/p>\n<p style=\"position:absolute;top:266px;left:788px;white-space:nowrap\" class=\"ft280\">&nbsp;&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:288px;left:157px;white-space:nowrap\" class=\"ft280\">measured.&nbsp;The&nbsp;lens&nbsp;is&nbsp;then moved to&nbsp;the&nbsp;conjugate&nbsp;position so&nbsp;that distinct&nbsp;diminished&nbsp;<\/p>\n<p style=\"position:absolute;top:310px;left:157px;white-space:nowrap\" class=\"ft280\">images&nbsp;are&nbsp;formed in the&nbsp;plane&nbsp;of the&nbsp;crosswire.&nbsp;Separation&nbsp;d<\/p>\n<p style=\"position:absolute;top:318px;left:627px;white-space:nowrap\" class=\"ft282\">2<\/p>\n<p style=\"position:absolute;top:310px;left:634px;white-space:nowrap\" class=\"ft280\">&nbsp;is&nbsp;measured.&nbsp;Since&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:332px;left:157px;white-space:nowrap\" class=\"ft280\">magnification&nbsp;m<\/p>\n<p style=\"position:absolute;top:340px;left:275px;white-space:nowrap\" class=\"ft282\">1<\/p>\n<p style=\"position:absolute;top:332px;left:281px;white-space:nowrap\" class=\"ft280\">&nbsp;in the&nbsp;first position&nbsp;is&nbsp;just inverse&nbsp;of the&nbsp;magnification m<\/p>\n<p style=\"position:absolute;top:340px;left:695px;white-space:nowrap\" class=\"ft282\">2<\/p>\n<p style=\"position:absolute;top:332px;left:701px;white-space:nowrap\" class=\"ft280\">&nbsp;,&nbsp;we&nbsp;have&nbsp;<\/p>\n<p style=\"position:absolute;top:354px;left:157px;white-space:nowrap\" class=\"ft284\">&nbsp;<br \/>d<\/p>\n<p style=\"position:absolute;top:388px;left:166px;white-space:nowrap\" class=\"ft282\">1<\/p>\n<p style=\"position:absolute;top:381px;left:172px;white-space:nowrap\" class=\"ft280\">&nbsp;\/&nbsp;d =&nbsp;d \/&nbsp;d<\/p>\n<p style=\"position:absolute;top:388px;left:246px;white-space:nowrap\" class=\"ft282\">2&nbsp;<\/p>\n<p style=\"position:absolute;top:402px;left:157px;white-space:nowrap\" class=\"ft285\">&nbsp;<br \/>d =&nbsp;(d<\/p>\n<p style=\"position:absolute;top:429px;left:200px;white-space:nowrap\" class=\"ft282\">1<\/p>\n<p style=\"position:absolute;top:423px;left:206px;white-space:nowrap\" class=\"ft280\">&nbsp;d<\/p>\n<p style=\"position:absolute;top:429px;left:219px;white-space:nowrap\" class=\"ft282\">2&nbsp;<\/p>\n<p style=\"position:absolute;top:423px;left:228px;white-space:nowrap\" class=\"ft280\">)<\/p>\n<p style=\"position:absolute;top:419px;left:234px;white-space:nowrap\" class=\"ft282\">1\/2&nbsp;<\/p>\n<p style=\"position:absolute;top:443px;left:157px;white-space:nowrap\" class=\"ft280\">&nbsp;<\/p>\n<p style=\"position:absolute;top:458px;left:157px;white-space:nowrap\" class=\"ft281\"><b>Determination of&nbsp;the&nbsp;wavelength of&nbsp;the&nbsp;light:&nbsp;&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:480px;left:157px;white-space:nowrap\" class=\"ft280\">In order&nbsp;to&nbsp;determine&nbsp;the&nbsp;wavelength of monochromatic&nbsp;light with the&nbsp;help of biprism,&nbsp;<\/p>\n<p style=\"position:absolute;top:502px;left:157px;white-space:nowrap\" class=\"ft280\">we&nbsp;employ&nbsp;the&nbsp;formula&nbsp;<\/p>\n<p style=\"position:absolute;top:524px;left:157px;white-space:nowrap\" class=\"ft280\">&nbsp;&lambda;&nbsp;=&nbsp;d\/D&nbsp;*&nbsp;&beta;&nbsp;<\/p>\n<p style=\"position:absolute;top:546px;left:157px;white-space:nowrap\" class=\"ft280\">The&nbsp;value&nbsp;of&nbsp;fringe&nbsp;width&nbsp;&beta;&nbsp;,&nbsp;the&nbsp;distance&nbsp;d&nbsp;between&nbsp;the&nbsp;virtual&nbsp;coherent&nbsp;S<\/p>\n<p style=\"position:absolute;top:555px;left:718px;white-space:nowrap\" class=\"ft282\">1<\/p>\n<p style=\"position:absolute;top:546px;left:724px;white-space:nowrap\" class=\"ft280\">&nbsp;and S<\/p>\n<p style=\"position:absolute;top:555px;left:771px;white-space:nowrap\" class=\"ft282\">2<\/p>\n<p style=\"position:absolute;top:546px;left:777px;white-space:nowrap\" class=\"ft280\">&nbsp;and&nbsp;<\/p>\n<p style=\"position:absolute;top:568px;left:157px;white-space:nowrap\" class=\"ft280\">the&nbsp;normal&nbsp;distance&nbsp;D of the&nbsp;plane&nbsp;of observation of the&nbsp;fringes&nbsp;from&nbsp;the&nbsp;slit should be&nbsp;<\/p>\n<p style=\"position:absolute;top:590px;left:157px;white-space:nowrap\" class=\"ft280\">measured after&nbsp;making&nbsp;a&nbsp;few adjustments&nbsp;in the&nbsp;apparatus.&nbsp;<\/p>\n<p style=\"position:absolute;top:612px;left:157px;white-space:nowrap\" class=\"ft286\"><b>&nbsp;<br \/><\/b>&nbsp;<\/p>\n<p style=\"position:absolute;top:678px;left:157px;white-space:nowrap\" class=\"ft283\"><b>DISPLACEMENT OF&nbsp;FRINGES WHEN&nbsp;A&nbsp;THIN&nbsp;GLASS SHEET IS INTRODUCED&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:703px;left:157px;white-space:nowrap\" class=\"ft283\"><b>IN THE&nbsp;PATH&nbsp;OF&nbsp;FRINGES<\/b><\/p>\n<p style=\"position:absolute;top:706px;left:371px;white-space:nowrap\" class=\"ft281\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:703px;left:375px;white-space:nowrap\" class=\"ft283\"><b>[RGPV\/&nbsp;,Dec2012&nbsp;(10)]&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:729px;left:157px;white-space:nowrap\" class=\"ft281\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:751px;left:157px;white-space:nowrap\" class=\"ft281\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:773px;left:157px;white-space:nowrap\" class=\"ft281\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:1096px;left:680px;white-space:nowrap\" class=\"ft281\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:1113px;left:157px;white-space:nowrap\" class=\"ft281\"><b>&nbsp;<\/b><\/p>\n<\/div>\n<div id=\"page29-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559029.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:455px;white-space:nowrap\" class=\"ft290\">5&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:157px;white-space:nowrap\" class=\"ft291\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:68px;left:157px;white-space:nowrap\" class=\"ft291\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:90px;left:157px;white-space:nowrap\" class=\"ft291\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:112px;left:157px;white-space:nowrap\" class=\"ft291\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:134px;left:157px;white-space:nowrap\" class=\"ft290\">if&nbsp;we&nbsp;introduce&nbsp;a&nbsp;thin film&nbsp;somewhere,&nbsp;<\/p>\n<p style=\"position:absolute;top:156px;left:157px;white-space:nowrap\" class=\"ft290\">RI&nbsp;=&nbsp;&mu;&nbsp;<\/p>\n<p style=\"position:absolute;top:178px;left:157px;white-space:nowrap\" class=\"ft290\">t&nbsp;= (s<\/p>\n<p style=\"position:absolute;top:186px;left:192px;white-space:nowrap\" class=\"ft292\">1<\/p>\n<p style=\"position:absolute;top:178px;left:198px;white-space:nowrap\" class=\"ft290\">&nbsp;p-&nbsp;t)\/&nbsp;c + t\/v&nbsp;<\/p>\n<p style=\"position:absolute;top:200px;left:157px;white-space:nowrap\" class=\"ft290\">= 1\/c (s<\/p>\n<p style=\"position:absolute;top:208px;left:210px;white-space:nowrap\" class=\"ft292\">1<\/p>\n<p style=\"position:absolute;top:200px;left:216px;white-space:nowrap\" class=\"ft290\">&nbsp;p-&nbsp;t&nbsp;+&nbsp;&mu;t)&nbsp;<\/p>\n<p style=\"position:absolute;top:222px;left:157px;white-space:nowrap\" class=\"ft290\">= ( s<\/p>\n<p style=\"position:absolute;top:230px;left:186px;white-space:nowrap\" class=\"ft292\">1<\/p>\n<p style=\"position:absolute;top:222px;left:192px;white-space:nowrap\" class=\"ft290\">&nbsp;p&nbsp;+&nbsp;t(&mu;&nbsp;&#8211;&nbsp;1))\/&nbsp;c&nbsp;<\/p>\n<p style=\"position:absolute;top:244px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:266px;left:157px;white-space:nowrap\" class=\"ft290\">Effective&nbsp;distance&nbsp;in&nbsp;air s1&nbsp;to&nbsp;p&nbsp;=&nbsp;(s<\/p>\n<p style=\"position:absolute;top:274px;left:407px;white-space:nowrap\" class=\"ft292\">1<\/p>\n<p style=\"position:absolute;top:266px;left:413px;white-space:nowrap\" class=\"ft290\">&nbsp;p-&nbsp;t&nbsp;+&nbsp;&mu;t)&nbsp;<\/p>\n<p style=\"position:absolute;top:288px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:310px;left:157px;white-space:nowrap\" class=\"ft290\">Effective distance s<\/p>\n<p style=\"position:absolute;top:318px;left:295px;white-space:nowrap\" class=\"ft292\">1<\/p>\n<p style=\"position:absolute;top:310px;left:301px;white-space:nowrap\" class=\"ft290\">&nbsp;to&nbsp;p&nbsp;=&nbsp;s<\/p>\n<p style=\"position:absolute;top:318px;left:358px;white-space:nowrap\" class=\"ft292\">1<\/p>\n<p style=\"position:absolute;top:310px;left:364px;white-space:nowrap\" class=\"ft290\">&nbsp;p&nbsp;+&nbsp;t(&mu;&nbsp;&#8211;&nbsp;1)&nbsp;<\/p>\n<p style=\"position:absolute;top:332px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:354px;left:157px;white-space:nowrap\" class=\"ft290\">If the&nbsp;film&nbsp;is&nbsp;absent,&nbsp;<\/p>\n<p style=\"position:absolute;top:376px;left:157px;white-space:nowrap\" class=\"ft290\">s<\/p>\n<p style=\"position:absolute;top:384px;left:164px;white-space:nowrap\" class=\"ft292\">1<\/p>\n<p style=\"position:absolute;top:376px;left:170px;white-space:nowrap\" class=\"ft290\">&nbsp;p<\/p>\n<p style=\"position:absolute;top:384px;left:183px;white-space:nowrap\" class=\"ft292\">&nbsp;<\/p>\n<p style=\"position:absolute;top:376px;left:186px;white-space:nowrap\" class=\"ft290\">= s<\/p>\n<p style=\"position:absolute;top:384px;left:206px;white-space:nowrap\" class=\"ft292\">2<\/p>\n<p style=\"position:absolute;top:376px;left:212px;white-space:nowrap\" class=\"ft290\">&nbsp;p&nbsp;<\/p>\n<p style=\"position:absolute;top:398px;left:157px;white-space:nowrap\" class=\"ft290\">with film&nbsp;present is&nbsp;not&nbsp;true,&nbsp;i.e.&nbsp;we&nbsp;will not&nbsp;get&nbsp;a central maximum at&nbsp;o&nbsp;due&nbsp;to&nbsp;the&nbsp;film.&nbsp;<\/p>\n<p style=\"position:absolute;top:420px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:442px;left:157px;white-space:nowrap\" class=\"ft290\">Path&nbsp;difference&nbsp;=&nbsp;t(&mu;&nbsp;&#8211;&nbsp;1)&nbsp;<\/p>\n<p style=\"position:absolute;top:464px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:486px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:486px;left:161px;white-space:nowrap\" class=\"ft293\">&Delta;<\/p>\n<p style=\"position:absolute;top:486px;left:171px;white-space:nowrap\" class=\"ft290\">&nbsp;=&nbsp;&#8211;&nbsp;s<\/p>\n<p style=\"position:absolute;top:494px;left:204px;white-space:nowrap\" class=\"ft292\">1<\/p>\n<p style=\"position:absolute;top:486px;left:211px;white-space:nowrap\" class=\"ft290\">&nbsp;p&nbsp;-t(&mu;&nbsp;&#8211;&nbsp;1) + s<\/p>\n<p style=\"position:absolute;top:494px;left:307px;white-space:nowrap\" class=\"ft292\">2<\/p>\n<p style=\"position:absolute;top:486px;left:314px;white-space:nowrap\" class=\"ft290\">&nbsp;p&nbsp;<\/p>\n<p style=\"position:absolute;top:507px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:529px;left:157px;white-space:nowrap\" class=\"ft290\">Assuming&nbsp;that the&nbsp;maxima&nbsp;shifts&nbsp;to&nbsp;the&nbsp;point O,&nbsp;<\/p>\n<p style=\"position:absolute;top:551px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:573px;left:157px;white-space:nowrap\" class=\"ft290\">s<\/p>\n<p style=\"position:absolute;top:582px;left:164px;white-space:nowrap\" class=\"ft292\">2<\/p>\n<p style=\"position:absolute;top:573px;left:170px;white-space:nowrap\" class=\"ft290\">O&nbsp;= effective path&nbsp;difference&nbsp;<\/p>\n<p style=\"position:absolute;top:595px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:617px;left:157px;white-space:nowrap\" class=\"ft290\">by&nbsp;the&nbsp;pythagoras&nbsp;theorem&nbsp;,&nbsp;<\/p>\n<p style=\"position:absolute;top:639px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:661px;left:157px;white-space:nowrap\" class=\"ft290\">s<\/p>\n<p style=\"position:absolute;top:670px;left:164px;white-space:nowrap\" class=\"ft292\">2<\/p>\n<p style=\"position:absolute;top:661px;left:170px;white-space:nowrap\" class=\"ft290\">O&nbsp;= D(1&nbsp;+ &frac12;(x + d)<\/p>\n<p style=\"position:absolute;top:659px;left:299px;white-space:nowrap\" class=\"ft292\">2<\/p>\n<p style=\"position:absolute;top:661px;left:305px;white-space:nowrap\" class=\"ft290\">&nbsp;\/D<\/p>\n<p style=\"position:absolute;top:670px;left:327px;white-space:nowrap\" class=\"ft292\">2<\/p>\n<p style=\"position:absolute;top:661px;left:333px;white-space:nowrap\" class=\"ft290\">)&nbsp;<\/p>\n<p style=\"position:absolute;top:683px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:705px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;path difference&nbsp;=&nbsp;2&nbsp;x&nbsp;d \/&nbsp;D&nbsp;<\/p>\n<p style=\"position:absolute;top:727px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:749px;left:157px;white-space:nowrap\" class=\"ft290\">2&nbsp;x&nbsp;d&nbsp;\/ D&nbsp;=&nbsp;t(&mu;&nbsp;&#8211;&nbsp;1)&nbsp;<\/p>\n<p style=\"position:absolute;top:771px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:793px;left:157px;white-space:nowrap\" class=\"ft290\">x<\/p>\n<p style=\"position:absolute;top:802px;left:164px;white-space:nowrap\" class=\"ft292\">&nbsp;<\/p>\n<p style=\"position:absolute;top:793px;left:169px;white-space:nowrap\" class=\"ft290\">can&nbsp;be&nbsp;measured&nbsp;experimentally&nbsp;and&nbsp;it&nbsp;is&nbsp;the&nbsp;shift&nbsp;in&nbsp;the&nbsp;fringes(central maxima)&nbsp;D&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:815px;left:157px;white-space:nowrap\" class=\"ft290\">the&nbsp;conjugate&nbsp;foci&nbsp;of lens.&nbsp;S<\/p>\n<p style=\"position:absolute;top:824px;left:357px;white-space:nowrap\" class=\"ft292\">1<\/p>\n<p style=\"position:absolute;top:815px;left:363px;white-space:nowrap\" class=\"ft290\">&nbsp;and S<\/p>\n<p style=\"position:absolute;top:824px;left:407px;white-space:nowrap\" class=\"ft292\">2<\/p>\n<p style=\"position:absolute;top:815px;left:413px;white-space:nowrap\" class=\"ft290\">&nbsp;are&nbsp;the&nbsp;positions&nbsp;of&nbsp;the&nbsp;slits.&nbsp;If&nbsp;we&nbsp;know the&nbsp;thickness&nbsp;<\/p>\n<p style=\"position:absolute;top:837px;left:157px;white-space:nowrap\" class=\"ft290\">t,&nbsp;the&nbsp;refractive&nbsp;index&nbsp;&mu;&nbsp;can&nbsp;be&nbsp;calculated.&nbsp;<\/p>\n<p style=\"position:absolute;top:859px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:881px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:903px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:925px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:948px;left:165px;white-space:nowrap\" class=\"ft290\">S.NO&nbsp;<\/p>\n<p style=\"position:absolute;top:948px;left:331px;white-space:nowrap\" class=\"ft290\">RGPV QUESTIONS&nbsp;<\/p>\n<p style=\"position:absolute;top:948px;left:631px;white-space:nowrap\" class=\"ft290\">Year&nbsp;<\/p>\n<p style=\"position:absolute;top:948px;left:737px;white-space:nowrap\" class=\"ft290\">Marks&nbsp;<\/p>\n<p style=\"position:absolute;top:970px;left:165px;white-space:nowrap\" class=\"ft290\">Q.1&nbsp;&nbsp;Describe&nbsp;Fresnel Biprism.&nbsp;Discuss&nbsp;the&nbsp;effect&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:992px;left:218px;white-space:nowrap\" class=\"ft290\">introducing&nbsp;thin mica&nbsp;sheet in&nbsp;the&nbsp;path of one&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:1014px;left:218px;white-space:nowrap\" class=\"ft290\">the&nbsp;interfering&nbsp;beam&nbsp;in a&nbsp;experiment.&nbsp;Deduce&nbsp;<\/p>\n<p style=\"position:absolute;top:1036px;left:218px;white-space:nowrap\" class=\"ft290\">the&nbsp;expression for&nbsp;displacement of fringes.&nbsp;<\/p>\n<p style=\"position:absolute;top:970px;left:612px;white-space:nowrap\" class=\"ft290\">Dec&nbsp;2012&nbsp;<\/p>\n<p style=\"position:absolute;top:970px;left:751px;white-space:nowrap\" class=\"ft290\">10&nbsp;<\/p>\n<p style=\"position:absolute;top:1059px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1081px;left:157px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1104px;left:108px;white-space:nowrap\" class=\"ft290\">&nbsp;<\/p>\n<\/div>\n<div id=\"page30-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559030.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:455px;white-space:nowrap\" class=\"ft300\">6&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft302\">&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:86px;left:411px;white-space:nowrap\" class=\"ft301\"><b>Unit-02\/Lecture-03&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:120px;left:157px;white-space:nowrap\" class=\"ft301\"><b>&nbsp;&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:142px;left:157px;white-space:nowrap\" class=\"ft301\"><b>INTERFERENCE&nbsp;IN THIN FILMS&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:164px;left:157px;white-space:nowrap\" class=\"ft301\"><b>Thin-film interference<\/b>&nbsp;occurs&nbsp;when inciden<a href=\"http:\/\/en.wikipedia.org\/wiki\/Light_wave\" target=\"_blank\" rel=\"noopener\">t&nbsp;light&nbsp;waves&nbsp;<\/a>reflected by&nbsp;the&nbsp;upper&nbsp;and lower&nbsp;<\/p>\n<p style=\"position:absolute;top:186px;left:157px;white-space:nowrap\" class=\"ft300\">boundaries&nbsp;of a<a href=\"http:\/\/en.wikipedia.org\/wiki\/Thin_film\" target=\"_blank\" rel=\"noopener\">&nbsp;thin film&nbsp;<\/a><a href=\"http:\/\/en.wikipedia.org\/wiki\/Interference_%28wave_propagation%29\" target=\"_blank\" rel=\"noopener\">interfere&nbsp;<\/a>with&nbsp;one&nbsp;another&nbsp;to&nbsp;form&nbsp;a&nbsp;new wave.&nbsp;Studying&nbsp;this&nbsp;<\/p>\n<p style=\"position:absolute;top:208px;left:157px;white-space:nowrap\" class=\"ft300\">new wave&nbsp;can reveal&nbsp;information about the&nbsp;surfaces&nbsp;from&nbsp;which its&nbsp;components&nbsp;<\/p>\n<p style=\"position:absolute;top:230px;left:157px;white-space:nowrap\" class=\"ft300\">reflected, including&nbsp;the&nbsp;thickness&nbsp;of&nbsp;the&nbsp;film&nbsp;or&nbsp;the&nbsp;effective<a href=\"http:\/\/en.wikipedia.org\/wiki\/Refractive_index\" target=\"_blank\" rel=\"noopener\">&nbsp;refractive&nbsp;index&nbsp;<\/a>of the&nbsp;film&nbsp;<\/p>\n<p style=\"position:absolute;top:252px;left:157px;white-space:nowrap\" class=\"ft300\">medium.&nbsp;<\/p>\n<p style=\"position:absolute;top:274px;left:149px;white-space:nowrap\" class=\"ft300\">&nbsp;<\/p>\n<p style=\"position:absolute;top:823px;left:747px;white-space:nowrap\" class=\"ft300\">&nbsp;<\/p>\n<p style=\"position:absolute;top:851px;left:149px;white-space:nowrap\" class=\"ft300\">&nbsp;<\/p>\n<p style=\"position:absolute;top:884px;left:157px;white-space:nowrap\" class=\"ft301\"><b>Theory&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:927px;left:157px;white-space:nowrap\" class=\"ft300\">As&nbsp;light strikes&nbsp;the&nbsp;surface&nbsp;of a&nbsp;film&nbsp;it is&nbsp;either&nbsp;transmitted or&nbsp;reflected at the&nbsp;upper&nbsp;<\/p>\n<p style=\"position:absolute;top:949px;left:157px;white-space:nowrap\" class=\"ft300\">surface.&nbsp;Light that is&nbsp;transmitted reaches&nbsp;the&nbsp;bottom&nbsp;surface&nbsp;and may&nbsp;once&nbsp;again be&nbsp;<\/p>\n<p style=\"position:absolute;top:971px;left:157px;white-space:nowrap\" class=\"ft300\">transmitted&nbsp;or&nbsp;reflected.&nbsp;The&nbsp;light reflected from&nbsp;the&nbsp;upper&nbsp;and lower&nbsp;surfaces&nbsp;will&nbsp;<\/p>\n<p style=\"position:absolute;top:993px;left:157px;white-space:nowrap\" class=\"ft300\">interfere.&nbsp;The&nbsp;degree&nbsp;of constructive&nbsp;or&nbsp;destructive&nbsp;interference&nbsp;between the&nbsp;two&nbsp;light&nbsp;<\/p>\n<p style=\"position:absolute;top:1015px;left:157px;white-space:nowrap\" class=\"ft300\">waves&nbsp;depends&nbsp;on the&nbsp;difference&nbsp;in their&nbsp;phase.&nbsp;This&nbsp;difference&nbsp;in&nbsp;turn depends&nbsp;on the&nbsp;<\/p>\n<p style=\"position:absolute;top:1037px;left:157px;white-space:nowrap\" class=\"ft300\">thickness&nbsp;of the&nbsp;film&nbsp;layer, the&nbsp;refractive&nbsp;index&nbsp;of the&nbsp;film, and the&nbsp;angle&nbsp;of incidence&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:1059px;left:157px;white-space:nowrap\" class=\"ft300\">the&nbsp;original wave&nbsp;on&nbsp;the&nbsp;film.&nbsp;Additionally,&nbsp;a&nbsp;phase&nbsp;shift&nbsp;of&nbsp;180&deg; or&nbsp;&nbsp;radians&nbsp;may&nbsp;be&nbsp;<\/p>\n<p style=\"position:absolute;top:1081px;left:157px;white-space:nowrap\" class=\"ft300\">introduced upon reflection&nbsp;at a&nbsp;boundary&nbsp;depending&nbsp;on&nbsp;the&nbsp;refractive&nbsp;indices&nbsp;of the&nbsp;<\/p>\n<p style=\"position:absolute;top:1103px;left:157px;white-space:nowrap\" class=\"ft300\">materials&nbsp;on either&nbsp;side&nbsp;of the&nbsp;boundary.&nbsp;This&nbsp;phase&nbsp;shift occurs&nbsp;if the&nbsp;refractive&nbsp;index&nbsp;of&nbsp;<\/p>\n<\/div>\n<div id=\"page31-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559031.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:455px;white-space:nowrap\" class=\"ft310\">7&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:157px;white-space:nowrap\" class=\"ft310\">the&nbsp;medium&nbsp;the&nbsp;light&nbsp;is&nbsp;travelling&nbsp;through&nbsp;is&nbsp;less&nbsp;than&nbsp;the&nbsp;refractive&nbsp;of&nbsp;the&nbsp;material&nbsp;it&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:69px;left:157px;white-space:nowrap\" class=\"ft310\">striking.&nbsp;In&nbsp;other&nbsp;words, if&nbsp;<\/p>\n<p style=\"position:absolute;top:69px;left:425px;white-space:nowrap\" class=\"ft310\">and&nbsp;the&nbsp;light&nbsp;is&nbsp;travelling&nbsp;from material&nbsp;1&nbsp;to&nbsp;material&nbsp;<\/p>\n<p style=\"position:absolute;top:91px;left:157px;white-space:nowrap\" class=\"ft310\">2, then a&nbsp;phase&nbsp;shift occurs&nbsp;upon reflection.&nbsp;The&nbsp;pattern&nbsp;of light that&nbsp;results&nbsp;from&nbsp;this&nbsp;<\/p>\n<p style=\"position:absolute;top:113px;left:157px;white-space:nowrap\" class=\"ft310\">interference&nbsp;can appear&nbsp;either&nbsp;as&nbsp;light and dark bands&nbsp;or&nbsp;as&nbsp;colorful&nbsp;bands&nbsp;depending&nbsp;<\/p>\n<p style=\"position:absolute;top:135px;left:157px;white-space:nowrap\" class=\"ft310\">upon the&nbsp;source&nbsp;of the&nbsp;incident light.&nbsp;<\/p>\n<p style=\"position:absolute;top:177px;left:157px;white-space:nowrap\" class=\"ft310\">Consider&nbsp;light incident&nbsp;on a&nbsp;thin&nbsp;film&nbsp;and reflected by&nbsp;both the&nbsp;upper&nbsp;and lower&nbsp;<\/p>\n<p style=\"position:absolute;top:199px;left:157px;white-space:nowrap\" class=\"ft310\">boundaries.&nbsp;The&nbsp;optical&nbsp;path difference&nbsp;(OPD)&nbsp;of the&nbsp;reflected light must be&nbsp;calculated in&nbsp;<\/p>\n<p style=\"position:absolute;top:221px;left:157px;white-space:nowrap\" class=\"ft310\">order&nbsp;to&nbsp;determine&nbsp;the&nbsp;condition for&nbsp;interference.&nbsp;Referring&nbsp;to&nbsp;the&nbsp;ray&nbsp;diagram above,&nbsp;<\/p>\n<p style=\"position:absolute;top:243px;left:157px;white-space:nowrap\" class=\"ft310\">the&nbsp;OPD between the&nbsp;two&nbsp;waves&nbsp;is&nbsp;the&nbsp;following:&nbsp;<\/p>\n<p style=\"position:absolute;top:294px;left:532px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:332px;left:157px;white-space:nowrap\" class=\"ft310\">Where,&nbsp;<\/p>\n<p style=\"position:absolute;top:410px;left:411px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:435px;left:438px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:480px;left:157px;white-space:nowrap\" class=\"ft310\">Usin<a href=\"http:\/\/en.wikipedia.org\/wiki\/Snells_law\" target=\"_blank\" rel=\"noopener\">g&nbsp;Snell&#8217;s&nbsp;Law,<\/a>&nbsp;<\/p>\n<p style=\"position:absolute;top:480px;left:495px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:563px;left:629px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:621px;left:485px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:645px;left:411px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:683px;left:157px;white-space:nowrap\" class=\"ft310\">Interference&nbsp;will&nbsp;be&nbsp;constructive&nbsp;if the&nbsp;optical&nbsp;path difference&nbsp;is&nbsp;equal&nbsp;to&nbsp;an integer&nbsp;<\/p>\n<p style=\"position:absolute;top:705px;left:157px;white-space:nowrap\" class=\"ft310\">multiple&nbsp;of the&nbsp;wavelength of light,&nbsp;&nbsp;.&nbsp;<\/p>\n<p style=\"position:absolute;top:754px;left:392px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:793px;left:157px;white-space:nowrap\" class=\"ft310\">This&nbsp;condition may&nbsp;change&nbsp;after&nbsp;considering&nbsp;possible&nbsp;phase&nbsp;shifts&nbsp;that&nbsp;occur&nbsp;upon&nbsp;<\/p>\n<p style=\"position:absolute;top:815px;left:157px;white-space:nowrap\" class=\"ft310\">reflection.&nbsp;<\/p>\n<p style=\"position:absolute;top:858px;left:157px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:891px;left:483px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:913px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:954px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:975px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:998px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1020px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1041px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1063px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1085px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1107px;left:108px;white-space:nowrap\" class=\"ft310\">&nbsp;<\/p>\n<\/div>\n<div id=\"page32-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559032.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:455px;white-space:nowrap\" class=\"ft320\">8&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft324\">&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:68px;left:412px;white-space:nowrap\" class=\"ft321\"><b>Unit-02\/Lecture-04&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:101px;left:157px;white-space:nowrap\" class=\"ft322\"><b>INTERFENCE&nbsp;IN&nbsp;WEDGE&nbsp;SHAPED&nbsp;FILMS&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:148px;left:157px;white-space:nowrap\" class=\"ft320\">If&nbsp;two&nbsp;glass&nbsp;plates&nbsp;are&nbsp;placed&nbsp;face&nbsp;to&nbsp;face&nbsp;<\/p>\n<p style=\"position:absolute;top:170px;left:157px;white-space:nowrap\" class=\"ft320\">with one&nbsp;end separated&nbsp;by&nbsp;a&nbsp;piece&nbsp;of tissue&nbsp;<\/p>\n<p style=\"position:absolute;top:192px;left:157px;white-space:nowrap\" class=\"ft320\">paper or thin&nbsp;metal foil&nbsp;an&nbsp;air wedge&nbsp;will be&nbsp;<\/p>\n<p style=\"position:absolute;top:214px;left:157px;white-space:nowrap\" class=\"ft320\">formed between them.&nbsp;If monochromatic&nbsp;<\/p>\n<p style=\"position:absolute;top:236px;left:157px;white-space:nowrap\" class=\"ft320\">light is&nbsp;shone&nbsp;on the&nbsp;plates&nbsp;a&nbsp;series&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:258px;left:157px;white-space:nowrap\" class=\"ft320\">straight-line&nbsp;fringes&nbsp;will be&nbsp;seen&nbsp;parallel to&nbsp;<\/p>\n<p style=\"position:absolute;top:280px;left:157px;white-space:nowrap\" class=\"ft320\">the&nbsp;line&nbsp;along&nbsp;which they&nbsp;touch (Figure&nbsp;1).&nbsp;<\/p>\n<p style=\"position:absolute;top:302px;left:157px;white-space:nowrap\" class=\"ft320\">This&nbsp;is&nbsp;due&nbsp;to&nbsp;interference&nbsp;by&nbsp;division&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:324px;left:157px;white-space:nowrap\" class=\"ft320\">amplitude, as&nbsp;with Newton&#8217;s&nbsp;rings.&nbsp;Some&nbsp;<\/p>\n<p style=\"position:absolute;top:346px;left:157px;white-space:nowrap\" class=\"ft320\">light&nbsp;is&nbsp;reflected&nbsp;from the&nbsp;bottom surface&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:368px;left:157px;white-space:nowrap\" class=\"ft320\">the&nbsp;top plate&nbsp;and some&nbsp;from&nbsp;the&nbsp;top&nbsp;surface&nbsp;<\/p>\n<p style=\"position:absolute;top:390px;left:157px;white-space:nowrap\" class=\"ft320\">of the&nbsp;bottom&nbsp;plate.&nbsp;<\/p>\n<p style=\"position:absolute;top:412px;left:157px;white-space:nowrap\" class=\"ft320\">&nbsp;<\/p>\n<p style=\"position:absolute;top:434px;left:157px;white-space:nowrap\" class=\"ft320\">To&nbsp;see&nbsp;the&nbsp;fringes&nbsp;clearly&nbsp;the&nbsp;angle&nbsp;must&nbsp;be&nbsp;small,&nbsp;something&nbsp;like&nbsp;4&nbsp;minutes&nbsp;of&nbsp;arc.&nbsp;You&nbsp;<\/p>\n<p style=\"position:absolute;top:456px;left:157px;white-space:nowrap\" class=\"ft320\">should&nbsp;also&nbsp;look&nbsp;for fringes&nbsp;close&nbsp;to&nbsp;the&nbsp;join&nbsp;of&nbsp;the&nbsp;plates&nbsp;where&nbsp;the&nbsp;air gap&nbsp;is&nbsp;smallest,&nbsp;<\/p>\n<p style=\"position:absolute;top:478px;left:157px;white-space:nowrap\" class=\"ft320\">since&nbsp;the&nbsp;fringes&nbsp;are&nbsp;not&nbsp;well&nbsp;defined for&nbsp;path differences&nbsp;of&nbsp;more&nbsp;than some&nbsp;hundred&nbsp;<\/p>\n<p style=\"position:absolute;top:500px;left:157px;white-space:nowrap\" class=\"ft320\">wavelengths&nbsp;(0.058 mm&nbsp;for&nbsp;sodium&nbsp;light&nbsp;&#8211;&nbsp;compare&nbsp;this&nbsp;with the&nbsp;thickness&nbsp;of a&nbsp;sheet&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:522px;left:157px;white-space:nowrap\" class=\"ft320\">paper).&nbsp;<\/p>\n<p style=\"position:absolute;top:544px;left:157px;white-space:nowrap\" class=\"ft320\">&nbsp;<\/p>\n<p style=\"position:absolute;top:566px;left:157px;white-space:nowrap\" class=\"ft320\">Consider&nbsp;a&nbsp;point&nbsp;a&nbsp;distance&nbsp;x&nbsp;from&nbsp;the&nbsp;join.&nbsp;Path&nbsp;difference&nbsp;=&nbsp;2e&nbsp;=&nbsp;2x&theta;&nbsp;<\/p>\n<p style=\"position:absolute;top:588px;left:157px;white-space:nowrap\" class=\"ft320\">where&nbsp;&theta;&nbsp;is the&nbsp;angle&nbsp;between&nbsp;the&nbsp;plates in&nbsp;radians (this angle&nbsp;is small,&nbsp;so&nbsp;tan&nbsp;&theta;&nbsp;=&nbsp;&theta;&nbsp;in&nbsp;<\/p>\n<p style=\"position:absolute;top:610px;left:157px;white-space:nowrap\" class=\"ft320\">radians).&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:632px;left:157px;white-space:nowrap\" class=\"ft320\">&nbsp;<\/p>\n<p style=\"position:absolute;top:654px;left:157px;white-space:nowrap\" class=\"ft320\">For&nbsp;an air&nbsp;wedge&nbsp;there&nbsp;is&nbsp;a&nbsp;phase&nbsp;change&nbsp;on reflection at the&nbsp;top surface&nbsp;of the&nbsp;lower&nbsp;<\/p>\n<p style=\"position:absolute;top:676px;left:157px;white-space:nowrap\" class=\"ft320\">plate&nbsp;and so&nbsp;<\/p>\n<p style=\"position:absolute;top:719px;left:157px;white-space:nowrap\" class=\"ft320\">2e&nbsp;=&nbsp;2x&theta;=<\/p>\n<p style=\"position:absolute;top:719px;left:227px;white-space:nowrap\" class=\"ft323\">&nbsp;<\/p>\n<p style=\"position:absolute;top:719px;left:231px;white-space:nowrap\" class=\"ft320\">m&lambda;&nbsp;&nbsp;&nbsp;for&nbsp;a&nbsp;dark&nbsp;fringe&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:762px;left:157px;white-space:nowrap\" class=\"ft320\">2e&nbsp;=&nbsp;2x&theta;=<\/p>\n<p style=\"position:absolute;top:762px;left:227px;white-space:nowrap\" class=\"ft323\">&nbsp;(<\/p>\n<p style=\"position:absolute;top:762px;left:237px;white-space:nowrap\" class=\"ft320\">(2m+1)&lambda;&nbsp; &nbsp;for a bright&nbsp;fringe&nbsp;<\/p>\n<p style=\"position:absolute;top:805px;left:157px;white-space:nowrap\" class=\"ft320\">The&nbsp;travelling&nbsp;microscope&nbsp;or&nbsp;the&nbsp;eye&nbsp;must be&nbsp;focused close&nbsp;to&nbsp;the&nbsp;upper&nbsp;surface&nbsp;of the&nbsp;<\/p>\n<p style=\"position:absolute;top:827px;left:157px;white-space:nowrap\" class=\"ft320\">air wedge&nbsp;since&nbsp;this&nbsp;is&nbsp;where&nbsp;the&nbsp;fringes&nbsp;are&nbsp;localised.&nbsp;<\/p>\n<p style=\"position:absolute;top:849px;left:157px;white-space:nowrap\" class=\"ft320\">&nbsp;<\/p>\n<p style=\"position:absolute;top:871px;left:157px;white-space:nowrap\" class=\"ft320\">Pressing&nbsp;down gently&nbsp;with your&nbsp;finger&nbsp;on the&nbsp;plates&nbsp;will&nbsp;move&nbsp;the&nbsp;interference&nbsp;pattern,&nbsp;<\/p>\n<p style=\"position:absolute;top:893px;left:157px;white-space:nowrap\" class=\"ft320\">since&nbsp;only&nbsp;a very&nbsp;small&nbsp;movement&nbsp;is&nbsp;needed&nbsp;to&nbsp;alter&nbsp;the&nbsp;path difference&nbsp;significantly.&nbsp;<\/p>\n<p style=\"position:absolute;top:914px;left:157px;white-space:nowrap\" class=\"ft320\">&nbsp;<\/p>\n<p style=\"position:absolute;top:937px;left:157px;white-space:nowrap\" class=\"ft320\">The&nbsp;vertical soap&nbsp;film is&nbsp;a good&nbsp;example&nbsp;of&nbsp;wedge&nbsp;fringes.&nbsp;As&nbsp;the&nbsp;soap&nbsp;drains&nbsp;to&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:958px;left:157px;white-space:nowrap\" class=\"ft320\">bottom&nbsp;of the&nbsp;film&nbsp;a&nbsp;wedge&nbsp;of very&nbsp;small&nbsp;angle&nbsp;is&nbsp;formed.&nbsp;When the&nbsp;top part goes&nbsp;black&nbsp;<\/p>\n<p style=\"position:absolute;top:980px;left:157px;white-space:nowrap\" class=\"ft320\">the&nbsp;film&nbsp;is&nbsp;about to&nbsp;break.&nbsp;The&nbsp;flatness&nbsp;of a&nbsp;glass&nbsp;surface&nbsp;may&nbsp;be&nbsp;tested&nbsp;by&nbsp;placing&nbsp;it&nbsp;on&nbsp;a&nbsp;<\/p>\n<p style=\"position:absolute;top:1002px;left:157px;white-space:nowrap\" class=\"ft320\">test surface&nbsp;which is&nbsp;known to&nbsp;be&nbsp;flat and illuminating&nbsp;them&nbsp;with monochromatic&nbsp;light;&nbsp;<\/p>\n<p style=\"position:absolute;top:1024px;left:157px;white-space:nowrap\" class=\"ft320\">any&nbsp;imperfections&nbsp;will show&nbsp;up&nbsp;as&nbsp;loop-shaped interference&nbsp;fringes&nbsp;around bumps&nbsp;or&nbsp;<\/p>\n<p style=\"position:absolute;top:1046px;left:157px;white-space:nowrap\" class=\"ft320\">depressions&nbsp;on the&nbsp;surfaces.&nbsp;<\/p>\n<p style=\"position:absolute;top:1069px;left:108px;white-space:nowrap\" class=\"ft320\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1109px;left:108px;white-space:nowrap\" class=\"ft320\">&nbsp;<\/p>\n<\/div>\n<div id=\"page33-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559033.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:455px;white-space:nowrap\" class=\"ft330\">9&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft335\">&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:86px;left:412px;white-space:nowrap\" class=\"ft331\"><b>Unit-02\/Lecture-05&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:120px;left:157px;white-space:nowrap\" class=\"ft331\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:141px;left:157px;white-space:nowrap\" class=\"ft332\"><b>MICHELSON&nbsp;INTERFEROMETER&nbsp;[RGPV\/&nbsp;June&nbsp;2012&nbsp;(7),Dec2013&nbsp;(14)]&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:189px;left:157px;white-space:nowrap\" class=\"ft330\">The&nbsp;<\/p>\n<p style=\"position:absolute;top:188px;left:199px;white-space:nowrap\" class=\"ft331\"><b>Michelson&nbsp;interferometer<\/b>&nbsp;&nbsp;is&nbsp;the&nbsp;most common configuration for&nbsp;optical&nbsp;<\/p>\n<p style=\"position:absolute;top:211px;left:157px;white-space:nowrap\" class=\"ft330\">interferometry&nbsp;and&nbsp;was&nbsp;invented&nbsp;by&nbsp;Albert&nbsp;Abraham Michelson.&nbsp;An&nbsp;interference&nbsp;pattern&nbsp;<\/p>\n<p style=\"position:absolute;top:233px;left:157px;white-space:nowrap\" class=\"ft330\">is&nbsp;produced by&nbsp;splitting&nbsp;a&nbsp;beam&nbsp;of&nbsp;light into&nbsp;two&nbsp;paths, bouncing&nbsp;the&nbsp;beams&nbsp;back and&nbsp;<\/p>\n<p style=\"position:absolute;top:255px;left:157px;white-space:nowrap\" class=\"ft330\">recombining&nbsp;them.&nbsp;The&nbsp;different paths&nbsp;may&nbsp;be&nbsp;of different lengths&nbsp;or&nbsp;be&nbsp;composed of&nbsp;<\/p>\n<p style=\"position:absolute;top:277px;left:157px;white-space:nowrap\" class=\"ft330\">different&nbsp;materials&nbsp;to&nbsp;create&nbsp;alternating&nbsp;interference&nbsp;fringes&nbsp;on&nbsp;a back&nbsp;detector.&nbsp;<\/p>\n<p style=\"position:absolute;top:319px;left:157px;white-space:nowrap\" class=\"ft331\"><b>Construction&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:363px;left:157px;white-space:nowrap\" class=\"ft330\">A Michelson&nbsp;interferometer consists&nbsp;of&nbsp;two&nbsp;highly&nbsp;polished&nbsp;mirrors&nbsp;M<\/p>\n<p style=\"position:absolute;top:371px;left:673px;white-space:nowrap\" class=\"ft333\">1<\/p>\n<p style=\"position:absolute;top:363px;left:679px;white-space:nowrap\" class=\"ft330\">&nbsp;&amp; M<\/p>\n<p style=\"position:absolute;top:371px;left:717px;white-space:nowrap\" class=\"ft333\">2<\/p>\n<p style=\"position:absolute;top:363px;left:723px;white-space:nowrap\" class=\"ft330\">. A&nbsp;source&nbsp;S&nbsp;<\/p>\n<p style=\"position:absolute;top:384px;left:157px;white-space:nowrap\" class=\"ft330\">emits&nbsp;monochromatic&nbsp;light that hits&nbsp;a&nbsp;half-silvered&nbsp;mirror,&nbsp;surface&nbsp;M,&nbsp;at&nbsp;point&nbsp;C.&nbsp;M&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:406px;left:157px;white-space:nowrap\" class=\"ft330\">partially&nbsp;reflective, so&nbsp;one&nbsp;beam&nbsp;is&nbsp;transmitted&nbsp;through to&nbsp;point B&nbsp;while&nbsp;one&nbsp;is&nbsp;reflected&nbsp;<\/p>\n<p style=\"position:absolute;top:428px;left:157px;white-space:nowrap\" class=\"ft330\">in the&nbsp;direction of A.&nbsp;Both beams&nbsp;recombine&nbsp;at point C&#8217;&nbsp;to&nbsp;produce an&nbsp;interference&nbsp;<\/p>\n<p style=\"position:absolute;top:450px;left:157px;white-space:nowrap\" class=\"ft330\">pattern&nbsp;(assuming&nbsp;proper alignment)&nbsp;visible&nbsp;to&nbsp;the&nbsp;observer at&nbsp;point&nbsp;E.&nbsp;To&nbsp;the&nbsp;observer at&nbsp;<\/p>\n<p style=\"position:absolute;top:472px;left:157px;white-space:nowrap\" class=\"ft330\">point E, the&nbsp;effects&nbsp;observed would be&nbsp;the&nbsp;same&nbsp;as&nbsp;those&nbsp;produced by&nbsp;placing&nbsp;surfaces&nbsp;A&nbsp;<\/p>\n<p style=\"position:absolute;top:494px;left:157px;white-space:nowrap\" class=\"ft330\">and B&#8217;&nbsp;(the&nbsp;image&nbsp;of B&nbsp;on the&nbsp;surface&nbsp;M)&nbsp;on top&nbsp;of each other.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:537px;left:157px;white-space:nowrap\" class=\"ft331\"><b>Working&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:580px;left:157px;white-space:nowrap\" class=\"ft330\">Light&nbsp;from a&nbsp;monochromatic&nbsp;source&nbsp;S is&nbsp;divided&nbsp;by&nbsp;a beam&nbsp;splitter&nbsp;(BS),&nbsp;which&nbsp;is&nbsp;oriented&nbsp;<\/p>\n<p style=\"position:absolute;top:602px;left:157px;white-space:nowrap\" class=\"ft330\">at&nbsp;an&nbsp;angle&nbsp;45&deg;&nbsp;to&nbsp;the&nbsp;beam, producing&nbsp;two&nbsp;beams&nbsp;of equal&nbsp;intensity.&nbsp;The&nbsp;transmitted&nbsp;<\/p>\n<p style=\"position:absolute;top:624px;left:157px;white-space:nowrap\" class=\"ft330\">beam (T)&nbsp;travels&nbsp;to&nbsp;mirror M<\/p>\n<p style=\"position:absolute;top:633px;left:367px;white-space:nowrap\" class=\"ft333\">1<\/p>\n<p style=\"position:absolute;top:624px;left:373px;white-space:nowrap\" class=\"ft330\">&nbsp;and it is&nbsp;reflected&nbsp;back to&nbsp;BS.&nbsp;50% of the&nbsp;returning&nbsp;beam&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:646px;left:157px;white-space:nowrap\" class=\"ft330\">then reflected by&nbsp;the&nbsp;beam&nbsp;splitter&nbsp;and strikes&nbsp;the&nbsp;screen,&nbsp;E.&nbsp;The&nbsp;reflected&nbsp;beam&nbsp;(R)&nbsp;<\/p>\n<p style=\"position:absolute;top:668px;left:157px;white-space:nowrap\" class=\"ft330\">travels&nbsp;to&nbsp;mirror M<\/p>\n<p style=\"position:absolute;top:677px;left:305px;white-space:nowrap\" class=\"ft333\">2<\/p>\n<p style=\"position:absolute;top:668px;left:311px;white-space:nowrap\" class=\"ft330\">,&nbsp;where&nbsp;it&nbsp;is&nbsp;reflected.&nbsp;50% of this&nbsp;beam&nbsp;passes&nbsp;straight through&nbsp;<\/p>\n<p style=\"position:absolute;top:690px;left:157px;white-space:nowrap\" class=\"ft330\">beam splitter and&nbsp;reaches&nbsp;the&nbsp;screen.&nbsp;<\/p>\n<p style=\"position:absolute;top:733px;left:157px;white-space:nowrap\" class=\"ft330\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:776px;left:157px;white-space:nowrap\" class=\"ft330\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:819px;left:157px;white-space:nowrap\" class=\"ft330\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:862px;left:157px;white-space:nowrap\" class=\"ft330\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:905px;left:157px;white-space:nowrap\" class=\"ft330\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:948px;left:157px;white-space:nowrap\" class=\"ft330\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:991px;left:157px;white-space:nowrap\" class=\"ft330\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:1034px;left:157px;white-space:nowrap\" class=\"ft330\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:1061px;left:157px;white-space:nowrap\" class=\"ft336\">&nbsp;&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:1115px;left:157px;white-space:nowrap\" class=\"ft330\">&nbsp;<\/p>\n<\/div>\n<div id=\"page34-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559034.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft340\">10&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft340\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:157px;white-space:nowrap\" class=\"ft340\">Since&nbsp;the&nbsp;reflecting&nbsp;surface&nbsp;of the&nbsp;beam&nbsp;splitter&nbsp;BS&nbsp;is&nbsp;the&nbsp;surface&nbsp;on the&nbsp;lower&nbsp;right, the&nbsp;<\/p>\n<p style=\"position:absolute;top:68px;left:157px;white-space:nowrap\" class=\"ft340\">light ray&nbsp;starting&nbsp;from&nbsp;the&nbsp;source&nbsp;S&nbsp;and undergoing&nbsp;reflection at the&nbsp;mirror&nbsp;M<\/p>\n<p style=\"position:absolute;top:76px;left:721px;white-space:nowrap\" class=\"ft341\">2<\/p>\n<p style=\"position:absolute;top:68px;left:727px;white-space:nowrap\" class=\"ft340\">&nbsp;passes&nbsp;<\/p>\n<p style=\"position:absolute;top:90px;left:157px;white-space:nowrap\" class=\"ft340\">through the&nbsp;beam&nbsp;splitter&nbsp;three&nbsp;times, while&nbsp;the&nbsp;ray&nbsp;reflected at M<\/p>\n<p style=\"position:absolute;top:98px;left:646px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:90px;left:652px;white-space:nowrap\" class=\"ft340\">&nbsp;travels&nbsp;through BS&nbsp;<\/p>\n<p style=\"position:absolute;top:112px;left:157px;white-space:nowrap\" class=\"ft340\">only&nbsp;once.&nbsp;The&nbsp;optical&nbsp;path length through the&nbsp;glass&nbsp;plate&nbsp;depends&nbsp;on its&nbsp;index&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:134px;left:157px;white-space:nowrap\" class=\"ft340\">refraction, which causes&nbsp;an optical&nbsp;path difference&nbsp;between the&nbsp;two&nbsp;beams.&nbsp;To&nbsp;<\/p>\n<p style=\"position:absolute;top:156px;left:157px;white-space:nowrap\" class=\"ft340\">compensate&nbsp;for&nbsp;this, a&nbsp;glass&nbsp;plate&nbsp;CP&nbsp;of the&nbsp;same&nbsp;thickness&nbsp;and index&nbsp;of refraction&nbsp;as&nbsp;<\/p>\n<p style=\"position:absolute;top:178px;left:157px;white-space:nowrap\" class=\"ft340\">that of BS&nbsp;is&nbsp;introduced between M<\/p>\n<p style=\"position:absolute;top:186px;left:416px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:178px;left:422px;white-space:nowrap\" class=\"ft340\">&nbsp;and&nbsp;BS.&nbsp;The&nbsp;recombined beams&nbsp;interfere&nbsp;and&nbsp;<\/p>\n<p style=\"position:absolute;top:200px;left:157px;white-space:nowrap\" class=\"ft340\">produce&nbsp;fringes&nbsp;at the&nbsp;screen E.&nbsp;The&nbsp;relative&nbsp;phase&nbsp;of the&nbsp;two&nbsp;beams&nbsp;determines&nbsp;<\/p>\n<p style=\"position:absolute;top:222px;left:157px;white-space:nowrap\" class=\"ft340\">whether&nbsp;the&nbsp;interference&nbsp;will&nbsp;be&nbsp;constructive&nbsp;or&nbsp;destructive.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:265px;left:157px;white-space:nowrap\" class=\"ft340\">From the&nbsp;screen,&nbsp;an&nbsp;observer sees M<\/p>\n<p style=\"position:absolute;top:273px;left:441px;white-space:nowrap\" class=\"ft341\">2<\/p>\n<p style=\"position:absolute;top:265px;left:447px;white-space:nowrap\" class=\"ft340\">&nbsp;directly&nbsp;and&nbsp;the&nbsp;virtual image&nbsp;M<\/p>\n<p style=\"position:absolute;top:273px;left:697px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:265px;left:703px;white-space:nowrap\" class=\"ft340\">&#8216;&nbsp;of&nbsp;the&nbsp;mirror&nbsp;<\/p>\n<p style=\"position:absolute;top:287px;left:157px;white-space:nowrap\" class=\"ft340\">M<\/p>\n<p style=\"position:absolute;top:295px;left:172px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:287px;left:178px;white-space:nowrap\" class=\"ft340\">,&nbsp;formed by&nbsp;reflection in the&nbsp;beam&nbsp;splitter, as&nbsp;shown in Fig.&nbsp;3.&nbsp;This&nbsp;means&nbsp;that one&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:309px;left:157px;white-space:nowrap\" class=\"ft340\">the&nbsp;interfering&nbsp;beams&nbsp;comes&nbsp;from&nbsp;M<\/p>\n<p style=\"position:absolute;top:317px;left:439px;white-space:nowrap\" class=\"ft341\">2<\/p>\n<p style=\"position:absolute;top:309px;left:445px;white-space:nowrap\" class=\"ft340\">&nbsp;and the&nbsp;other&nbsp;beam&nbsp;appears&nbsp;to&nbsp;come&nbsp;from&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:331px;left:157px;white-space:nowrap\" class=\"ft340\">virtual image&nbsp;M<\/p>\n<p style=\"position:absolute;top:339px;left:272px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:331px;left:278px;white-space:nowrap\" class=\"ft340\">&#8216;.&nbsp;If the&nbsp;two&nbsp;arms&nbsp;of&nbsp;the&nbsp;interferometer&nbsp;are&nbsp;equal&nbsp;in&nbsp;length, M<\/p>\n<p style=\"position:absolute;top:339px;left:728px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:331px;left:734px;white-space:nowrap\" class=\"ft340\">&#8216;&nbsp;coincides&nbsp;<\/p>\n<p style=\"position:absolute;top:353px;left:157px;white-space:nowrap\" class=\"ft340\">with M<\/p>\n<p style=\"position:absolute;top:361px;left:209px;white-space:nowrap\" class=\"ft341\">2<\/p>\n<p style=\"position:absolute;top:353px;left:215px;white-space:nowrap\" class=\"ft340\">.&nbsp;If they&nbsp;do&nbsp;not coincide, let&nbsp;the&nbsp;distance&nbsp;between&nbsp;them&nbsp;be&nbsp;<i>d<\/i>,&nbsp;and&nbsp;consider a&nbsp;light&nbsp;<\/p>\n<p style=\"position:absolute;top:375px;left:157px;white-space:nowrap\" class=\"ft340\">ray&nbsp;from&nbsp;a&nbsp;point S.&nbsp;It will&nbsp;be&nbsp;reflected by&nbsp;both M<\/p>\n<p style=\"position:absolute;top:383px;left:514px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:375px;left:520px;white-space:nowrap\" class=\"ft340\">&#8216;&nbsp;and M<\/p>\n<p style=\"position:absolute;top:383px;left:576px;white-space:nowrap\" class=\"ft341\">2<\/p>\n<p style=\"position:absolute;top:375px;left:582px;white-space:nowrap\" class=\"ft340\">, and the&nbsp;observer&nbsp;will&nbsp;see&nbsp;two&nbsp;<\/p>\n<p style=\"position:absolute;top:397px;left:157px;white-space:nowrap\" class=\"ft340\">virtual images,&nbsp;S<\/p>\n<p style=\"position:absolute;top:405px;left:280px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:397px;left:286px;white-space:nowrap\" class=\"ft340\">&nbsp;due&nbsp;to&nbsp;reflection at M<\/p>\n<p style=\"position:absolute;top:405px;left:458px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:397px;left:464px;white-space:nowrap\" class=\"ft340\">&#8216;,&nbsp;and S<\/p>\n<p style=\"position:absolute;top:405px;left:519px;white-space:nowrap\" class=\"ft341\">2<\/p>\n<p style=\"position:absolute;top:397px;left:525px;white-space:nowrap\" class=\"ft340\">&nbsp;due&nbsp;to&nbsp;reflection at&nbsp;M<\/p>\n<p style=\"position:absolute;top:405px;left:697px;white-space:nowrap\" class=\"ft341\">2<\/p>\n<p style=\"position:absolute;top:397px;left:703px;white-space:nowrap\" class=\"ft340\">. These&nbsp;virtual&nbsp;<\/p>\n<p style=\"position:absolute;top:419px;left:157px;white-space:nowrap\" class=\"ft340\">images&nbsp;will be&nbsp;separated&nbsp;by&nbsp;a distance&nbsp;2<i>d<\/i>. If&nbsp;<i>&theta;<\/i>&nbsp;is&nbsp;the&nbsp;angle&nbsp;with which the&nbsp;observer&nbsp;looks&nbsp;<\/p>\n<p style=\"position:absolute;top:441px;left:157px;white-space:nowrap\" class=\"ft340\">into&nbsp;the&nbsp;system, the&nbsp;path difference&nbsp;between the&nbsp;two&nbsp;beams&nbsp;is&nbsp;2<i>d<\/i>cos<i>&theta;<\/i>.&nbsp;When the&nbsp;light&nbsp;<\/p>\n<p style=\"position:absolute;top:463px;left:157px;white-space:nowrap\" class=\"ft340\">that comes&nbsp;from&nbsp;M<\/p>\n<p style=\"position:absolute;top:471px;left:308px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:463px;left:314px;white-space:nowrap\" class=\"ft340\">&nbsp;&nbsp;undergoes&nbsp;reflection at&nbsp;BS, a&nbsp;phase&nbsp;change&nbsp;of&nbsp;<i>&pi;<\/i>&nbsp;&nbsp;occurs, which&nbsp;<\/p>\n<p style=\"position:absolute;top:485px;left:157px;white-space:nowrap\" class=\"ft340\">corresponds&nbsp;to&nbsp;a&nbsp;path&nbsp;difference&nbsp;of&nbsp;&lambda;\/2.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:533px;left:157px;white-space:nowrap\" class=\"ft343\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:568px;left:157px;white-space:nowrap\" class=\"ft340\">Therefore, the&nbsp;total&nbsp;path difference&nbsp;between the&nbsp;two&nbsp;beams&nbsp;is,&nbsp;<\/p>\n<p style=\"position:absolute;top:645px;left:157px;white-space:nowrap\" class=\"ft340\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:645px;left:303px;white-space:nowrap\" class=\"ft340\">&nbsp;<\/p>\n<p style=\"position:absolute;top:688px;left:157px;white-space:nowrap\" class=\"ft340\">The&nbsp;condition for&nbsp;constructive&nbsp;interference&nbsp;is&nbsp;then,&nbsp;<\/p>\n<p style=\"position:absolute;top:765px;left:157px;white-space:nowrap\" class=\"ft340\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:765px;left:662px;white-space:nowrap\" class=\"ft340\">&nbsp;<\/p>\n<p style=\"position:absolute;top:808px;left:157px;white-space:nowrap\" class=\"ft340\">For&nbsp;a given&nbsp;mirror separation&nbsp;<i>d<\/i>,&nbsp;a given&nbsp;wavelength&nbsp;<i>&lambda;<\/i>,&nbsp;and&nbsp;order&nbsp;<i>m<\/i>, the&nbsp;angle&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:830px;left:157px;white-space:nowrap\" class=\"ft340\">inclination&nbsp;<i>&theta;<\/i>&nbsp;&nbsp;is&nbsp;a constant,&nbsp;and&nbsp;the&nbsp;fringes&nbsp;are&nbsp;circular.&nbsp;They&nbsp;are&nbsp;called&nbsp;<i>fringes of&nbsp;equal&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:852px;left:157px;white-space:nowrap\" class=\"ft342\"><i>inclination<\/i>,&nbsp;or&nbsp;<i>Haidinger&nbsp;fringes<\/i>. If&nbsp;M<\/p>\n<p style=\"position:absolute;top:860px;left:425px;white-space:nowrap\" class=\"ft341\">1<\/p>\n<p style=\"position:absolute;top:852px;left:431px;white-space:nowrap\" class=\"ft340\">&#8216;&nbsp;coincides&nbsp;with M<\/p>\n<p style=\"position:absolute;top:860px;left:563px;white-space:nowrap\" class=\"ft341\">2<\/p>\n<p style=\"position:absolute;top:852px;left:569px;white-space:nowrap\" class=\"ft340\">,&nbsp;<i>d<\/i>&nbsp;=&nbsp;0, and the&nbsp;path difference&nbsp;<\/p>\n<p style=\"position:absolute;top:874px;left:157px;white-space:nowrap\" class=\"ft340\">between the&nbsp;interfering&nbsp;beams&nbsp;will&nbsp;be&nbsp;<i>&lambda;<\/i>\/2.&nbsp;This&nbsp;corresponds&nbsp;to&nbsp;destructive&nbsp;interference,&nbsp;<\/p>\n<p style=\"position:absolute;top:896px;left:157px;white-space:nowrap\" class=\"ft340\">so&nbsp;the&nbsp;center&nbsp;of the&nbsp;field will&nbsp;be&nbsp;dark.&nbsp;<\/p>\n<p style=\"position:absolute;top:939px;left:157px;white-space:nowrap\" class=\"ft340\">If one&nbsp;of&nbsp;the&nbsp;mirrors&nbsp;is&nbsp;moved through a&nbsp;distance&nbsp;<i>&lambda;<\/i>\/4, the&nbsp;path difference&nbsp;changes&nbsp;by&nbsp;<i>&lambda;<\/i>\/2&nbsp;<\/p>\n<p style=\"position:absolute;top:961px;left:157px;white-space:nowrap\" class=\"ft340\">and a&nbsp;maximum is&nbsp;obtained.&nbsp;If&nbsp;the&nbsp;mirror is&nbsp;moved&nbsp;through&nbsp;another&nbsp;<i>&lambda;<\/i>\/4,&nbsp;a minimum&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:983px;left:157px;white-space:nowrap\" class=\"ft340\">obtained;&nbsp;moving&nbsp;it by&nbsp;another&nbsp;<i>&lambda;<\/i>\/4,&nbsp;again&nbsp;a maximum is&nbsp;obtained&nbsp;and&nbsp;so&nbsp;on.&nbsp;Because&nbsp;<i>d<\/i>&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:1005px;left:157px;white-space:nowrap\" class=\"ft340\">multiplied&nbsp;by&nbsp;cos<i>&theta;<\/i>,&nbsp;as&nbsp;<i>d<\/i>&nbsp;increases, new rings&nbsp;appear&nbsp;in the&nbsp;center&nbsp;faster&nbsp;than the&nbsp;rings&nbsp;<\/p>\n<p style=\"position:absolute;top:1027px;left:157px;white-space:nowrap\" class=\"ft340\">already&nbsp;present at the&nbsp;periphery&nbsp;disappear, and&nbsp;the&nbsp;field becomes&nbsp;more&nbsp;crowded with&nbsp;<\/p>\n<p style=\"position:absolute;top:1048px;left:157px;white-space:nowrap\" class=\"ft340\">thinner&nbsp;rings&nbsp;toward the&nbsp;outside.&nbsp;If&nbsp;<i>d<\/i>&nbsp;decreases,&nbsp;the&nbsp;rings&nbsp;contract, become&nbsp;wider&nbsp;and&nbsp;<\/p>\n<p style=\"position:absolute;top:1070px;left:157px;white-space:nowrap\" class=\"ft340\">more&nbsp;sparsely&nbsp;distributed, and disappear&nbsp;at the&nbsp;center.&nbsp;<\/p>\n<p style=\"position:absolute;top:1114px;left:157px;white-space:nowrap\" class=\"ft343\">&nbsp;&nbsp;<\/p>\n<\/div>\n<div id=\"page35-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559035.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft350\">11&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft350\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:157px;white-space:nowrap\" class=\"ft350\">For destructive&nbsp;interference, the&nbsp;total&nbsp;path difference&nbsp;must be&nbsp;an integer&nbsp;number&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:68px;left:157px;white-space:nowrap\" class=\"ft350\">wavelengths&nbsp;plus&nbsp;a&nbsp;half&nbsp;wavelength,&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:141px;left:157px;white-space:nowrap\" class=\"ft350\">&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:141px;left:556px;white-space:nowrap\" class=\"ft350\">&nbsp;<\/p>\n<p style=\"position:absolute;top:183px;left:157px;white-space:nowrap\" class=\"ft350\">If the&nbsp;images&nbsp;S<\/p>\n<p style=\"position:absolute;top:192px;left:263px;white-space:nowrap\" class=\"ft351\">1<\/p>\n<p style=\"position:absolute;top:183px;left:269px;white-space:nowrap\" class=\"ft350\">&nbsp;and S<\/p>\n<p style=\"position:absolute;top:192px;left:313px;white-space:nowrap\" class=\"ft351\">2<\/p>\n<p style=\"position:absolute;top:183px;left:319px;white-space:nowrap\" class=\"ft350\">&nbsp;from the&nbsp;two&nbsp;mirrors&nbsp;are&nbsp;exactly&nbsp;the&nbsp;same&nbsp;distance&nbsp;away,&nbsp;<i>d<\/i>=0&nbsp;and&nbsp;<\/p>\n<p style=\"position:absolute;top:205px;left:157px;white-space:nowrap\" class=\"ft350\">there&nbsp;is&nbsp;no&nbsp;dependance&nbsp;on&nbsp;<i>&theta;.&nbsp;<\/i>This&nbsp;means&nbsp;that only&nbsp;one&nbsp;fringe&nbsp;is&nbsp;visible,&nbsp;the&nbsp;zero&nbsp;order&nbsp;<\/p>\n<p style=\"position:absolute;top:227px;left:157px;white-space:nowrap\" class=\"ft350\">destructive&nbsp;interfrence&nbsp;fringe, where&nbsp;<\/p>\n<p style=\"position:absolute;top:314px;left:157px;white-space:nowrap\" class=\"ft353\">&nbsp;<\/p>\n<p style=\"position:absolute;top:314px;left:406px;white-space:nowrap\" class=\"ft353\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:355px;left:157px;white-space:nowrap\" class=\"ft353\">&nbsp;<\/p>\n<p style=\"position:absolute;top:396px;left:157px;white-space:nowrap\" class=\"ft354\">&nbsp;<\/p>\n<p style=\"position:absolute;top:438px;left:157px;white-space:nowrap\" class=\"ft355\"><b>APPLICATION&nbsp;OF&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:438px;left:306px;white-space:nowrap\" class=\"ft356\"><b>MICHELSON&rsquo;S&nbsp;INTERFEROMETER&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:485px;left:157px;white-space:nowrap\" class=\"ft356\"><b>i)Determination of&nbsp;wavelength of&nbsp;light&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:532px;left:157px;white-space:nowrap\" class=\"ft350\">Using&nbsp;the&nbsp;Michelson interferometer, the&nbsp;wavelength of light from&nbsp;a&nbsp;monochromatic&nbsp;<\/p>\n<p style=\"position:absolute;top:554px;left:157px;white-space:nowrap\" class=\"ft350\">source&nbsp;can be&nbsp;determined.&nbsp;If&nbsp;M<\/p>\n<p style=\"position:absolute;top:562px;left:392px;white-space:nowrap\" class=\"ft351\">1<\/p>\n<p style=\"position:absolute;top:554px;left:398px;white-space:nowrap\" class=\"ft350\">&nbsp;is&nbsp;moved&nbsp;forward&nbsp;or backward,&nbsp;circular fringes&nbsp;appear&nbsp;<\/p>\n<p style=\"position:absolute;top:576px;left:157px;white-space:nowrap\" class=\"ft350\">or&nbsp;disappear&nbsp;at the&nbsp;centre.&nbsp;The&nbsp;mirror&nbsp;is&nbsp;moved through a&nbsp;known distance&nbsp;<i>x<\/i>&nbsp;&nbsp;and the&nbsp;<\/p>\n<p style=\"position:absolute;top:598px;left:157px;white-space:nowrap\" class=\"ft350\">number&nbsp;<i>n<\/i>&nbsp;of fringes&nbsp;appearing&nbsp;or&nbsp;disappearing&nbsp;at the&nbsp;centre&nbsp;is&nbsp;counted.&nbsp;For&nbsp;one&nbsp;fringe&nbsp;to&nbsp;<\/p>\n<p style=\"position:absolute;top:620px;left:157px;white-space:nowrap\" class=\"ft350\">appear&nbsp;or&nbsp;disappear,&nbsp;the&nbsp;mirror&nbsp;must&nbsp;be&nbsp;moved&nbsp;through&nbsp;a&nbsp;distance&nbsp;of&nbsp;&lambda;\/2.&nbsp;Knowing&nbsp;this,&nbsp;<\/p>\n<p style=\"position:absolute;top:642px;left:157px;white-space:nowrap\" class=\"ft350\">we&nbsp;can write,&nbsp;<\/p>\n<p style=\"position:absolute;top:685px;left:157px;white-space:nowrap\" class=\"ft350\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;n<i>&nbsp;&lambda;=<\/i>2x<i>&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:728px;left:157px;white-space:nowrap\" class=\"ft350\">&nbsp;<\/p>\n<p style=\"position:absolute;top:771px;left:157px;white-space:nowrap\" class=\"ft350\">so&nbsp;that the&nbsp;wavelength&nbsp;is<\/p>\n<p style=\"position:absolute;top:772px;left:340px;white-space:nowrap\" class=\"ft353\">,&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:814px;left:157px;white-space:nowrap\" class=\"ft350\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<i>&lambda;=&nbsp;<\/i>2x\/n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:856px;left:157px;white-space:nowrap\" class=\"ft356\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:903px;left:157px;white-space:nowrap\" class=\"ft356\"><b>ii)&nbsp;Difference between two&nbsp;close wavelengths:-&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:950px;left:157px;white-space:nowrap\" class=\"ft354\">It&nbsp;works&nbsp;by&nbsp;taking&nbsp;a beam of&nbsp;light&nbsp;from a source&nbsp;and&nbsp;splitting&nbsp;it&nbsp;into&nbsp;2,&nbsp;each&nbsp;beam of&nbsp;<\/p>\n<p style=\"position:absolute;top:972px;left:157px;white-space:nowrap\" class=\"ft354\">equal&nbsp;intensity.&nbsp;A&nbsp;path difference&nbsp;of 2d is&nbsp;introduced to&nbsp;one&nbsp;beam, then&nbsp;both beams&nbsp;are&nbsp;<\/p>\n<p style=\"position:absolute;top:994px;left:157px;white-space:nowrap\" class=\"ft354\">recombined&nbsp;at the&nbsp;beam&nbsp;splitter.&nbsp;The&nbsp;recombined beam&nbsp;is&nbsp;then reflected to&nbsp;an&nbsp;observer&nbsp;<\/p>\n<p style=\"position:absolute;top:1016px;left:157px;white-space:nowrap\" class=\"ft354\">and an interference&nbsp;pattern is&nbsp;observed.&nbsp;<\/p>\n<p style=\"position:absolute;top:1038px;left:157px;white-space:nowrap\" class=\"ft354\">&nbsp;For&nbsp;two&nbsp;monochromatic&nbsp;light sources, much like&nbsp;the&nbsp;sodium&nbsp;lamp used in this&nbsp;<\/p>\n<p style=\"position:absolute;top:1060px;left:157px;white-space:nowrap\" class=\"ft354\">experiment&nbsp;<\/p>\n<p style=\"position:absolute;top:1103px;left:157px;white-space:nowrap\" class=\"ft354\">dark fringes&nbsp;will&nbsp;occur&nbsp;when the&nbsp;optical&nbsp;path difference, d, is:&nbsp;<\/p>\n<\/div>\n<div id=\"page36-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559036.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft360\">12&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft360\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:157px;white-space:nowrap\" class=\"ft361\">2d&nbsp;=&nbsp;m<\/p>\n<p style=\"position:absolute;top:54px;left:207px;white-space:nowrap\" class=\"ft362\">1<\/p>\n<p style=\"position:absolute;top:46px;left:213px;white-space:nowrap\" class=\"ft361\">&lambda;<\/p>\n<p style=\"position:absolute;top:54px;left:221px;white-space:nowrap\" class=\"ft362\">1<\/p>\n<p style=\"position:absolute;top:46px;left:227px;white-space:nowrap\" class=\"ft361\">= m<\/p>\n<p style=\"position:absolute;top:54px;left:255px;white-space:nowrap\" class=\"ft362\">2<\/p>\n<p style=\"position:absolute;top:46px;left:261px;white-space:nowrap\" class=\"ft361\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:54px;left:273px;white-space:nowrap\" class=\"ft362\">2<\/p>\n<p style=\"position:absolute;top:46px;left:279px;white-space:nowrap\" class=\"ft361\">&nbsp;(1)&nbsp;<\/p>\n<p style=\"position:absolute;top:89px;left:157px;white-space:nowrap\" class=\"ft361\">However&nbsp;this&nbsp;only&nbsp;applies&nbsp;when wavelength&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:98px;left:489px;white-space:nowrap\" class=\"ft362\">1<\/p>\n<p style=\"position:absolute;top:89px;left:495px;white-space:nowrap\" class=\"ft361\">&asymp;&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:98px;left:517px;white-space:nowrap\" class=\"ft362\">2<\/p>\n<p style=\"position:absolute;top:89px;left:523px;white-space:nowrap\" class=\"ft361\">&nbsp;<\/p>\n<p style=\"position:absolute;top:132px;left:157px;white-space:nowrap\" class=\"ft361\">and where&nbsp;m<\/p>\n<p style=\"position:absolute;top:140px;left:253px;white-space:nowrap\" class=\"ft362\">1&nbsp;<\/p>\n<p style=\"position:absolute;top:132px;left:262px;white-space:nowrap\" class=\"ft361\">and m<\/p>\n<p style=\"position:absolute;top:140px;left:308px;white-space:nowrap\" class=\"ft362\">2&nbsp;<\/p>\n<p style=\"position:absolute;top:132px;left:316px;white-space:nowrap\" class=\"ft361\">are integers.&nbsp;<\/p>\n<p style=\"position:absolute;top:175px;left:157px;white-space:nowrap\" class=\"ft361\">From&nbsp;equation (1)&nbsp;the&nbsp;difference&nbsp;in wavelength can be&nbsp;obtained where:&nbsp;<\/p>\n<p style=\"position:absolute;top:226px;left:157px;white-space:nowrap\" class=\"ft361\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&#8710;&lambda;=&nbsp;<\/p>\n<p style=\"position:absolute;top:222px;left:276px;white-space:nowrap\" class=\"ft363\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:227px;left:285px;white-space:nowrap\" class=\"ft364\">m<\/p>\n<p style=\"position:absolute;top:218px;left:285px;white-space:nowrap\" class=\"ft364\">2<\/p>\n<p style=\"position:absolute;top:242px;left:274px;white-space:nowrap\" class=\"ft363\">2&#8710;&#119889;&#119889;<\/p>\n<p style=\"position:absolute;top:228px;left:298px;white-space:nowrap\" class=\"ft361\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)&nbsp;<\/p>\n<p style=\"position:absolute;top:273px;left:157px;white-space:nowrap\" class=\"ft361\">Where&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:282px;left:219px;white-space:nowrap\" class=\"ft362\">m<\/p>\n<p style=\"position:absolute;top:273px;left:228px;white-space:nowrap\" class=\"ft361\">&nbsp;is&nbsp;the&nbsp;mean&nbsp;wavelength&nbsp;of&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:282px;left:437px;white-space:nowrap\" class=\"ft362\">1<\/p>\n<p style=\"position:absolute;top:273px;left:443px;white-space:nowrap\" class=\"ft361\">,&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:282px;left:460px;white-space:nowrap\" class=\"ft362\">2<\/p>\n<p style=\"position:absolute;top:273px;left:466px;white-space:nowrap\" class=\"ft361\">&nbsp;and&nbsp;&Delta;d&nbsp;is the&nbsp;mirror&nbsp;shit.&nbsp;<\/p>\n<p style=\"position:absolute;top:295px;left:157px;white-space:nowrap\" class=\"ft361\">&nbsp;<\/p>\n<p style=\"position:absolute;top:338px;left:157px;white-space:nowrap\" class=\"ft365\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:360px;left:157px;white-space:nowrap\" class=\"ft360\">&nbsp;<\/p>\n<p style=\"position:absolute;top:383px;left:108px;white-space:nowrap\" class=\"ft360\">&nbsp;<\/p>\n<p style=\"position:absolute;top:421px;left:157px;white-space:nowrap\" class=\"ft360\">S.NO&nbsp;<\/p>\n<p style=\"position:absolute;top:421px;left:362px;white-space:nowrap\" class=\"ft360\">RGPV QUESTIONS&nbsp;<\/p>\n<p style=\"position:absolute;top:421px;left:670px;white-space:nowrap\" class=\"ft360\">Year&nbsp;<\/p>\n<p style=\"position:absolute;top:421px;left:745px;white-space:nowrap\" class=\"ft360\">Marks&nbsp;<\/p>\n<p style=\"position:absolute;top:444px;left:157px;white-space:nowrap\" class=\"ft360\">Q.1&nbsp;&nbsp;Describe&nbsp;the&nbsp;construction and working&nbsp;of&nbsp;Michelson&rsquo;s&nbsp;<\/p>\n<p style=\"position:absolute;top:466px;left:209px;white-space:nowrap\" class=\"ft360\">interferometer.&nbsp;Explain&nbsp;the&nbsp;principle&nbsp;of&nbsp;formation&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:488px;left:209px;white-space:nowrap\" class=\"ft360\">circular fringes.&nbsp;<\/p>\n<p style=\"position:absolute;top:444px;left:662px;white-space:nowrap\" class=\"ft360\">Dec&nbsp;<\/p>\n<p style=\"position:absolute;top:466px;left:662px;white-space:nowrap\" class=\"ft360\">2013&nbsp;<\/p>\n<p style=\"position:absolute;top:444px;left:725px;white-space:nowrap\" class=\"ft360\">7&nbsp;<\/p>\n<p style=\"position:absolute;top:510px;left:157px;white-space:nowrap\" class=\"ft360\">Q.2&nbsp;&nbsp;Describe&nbsp;&nbsp;Michelson&rsquo;s&nbsp;interferometer and&nbsp;how&nbsp;will you&nbsp;<\/p>\n<p style=\"position:absolute;top:532px;left:209px;white-space:nowrap\" class=\"ft360\">measure&nbsp;small&nbsp;difference&nbsp;in wavelengths&nbsp;of two&nbsp;waves&nbsp;with&nbsp;<\/p>\n<p style=\"position:absolute;top:554px;left:209px;white-space:nowrap\" class=\"ft360\">Michelson&rsquo;s&nbsp;interferometer.&nbsp;Calculate the distance between&nbsp;<\/p>\n<p style=\"position:absolute;top:576px;left:209px;white-space:nowrap\" class=\"ft360\">the&nbsp;two&nbsp;successive&nbsp;positions&nbsp;of&nbsp;a movable&nbsp;mirror of&nbsp;<\/p>\n<p style=\"position:absolute;top:598px;left:209px;white-space:nowrap\" class=\"ft360\">Michelson&rsquo;s&nbsp;interferometer giving&nbsp;best&nbsp;fringes&nbsp;in&nbsp;the&nbsp;case&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:620px;left:209px;white-space:nowrap\" class=\"ft360\">sodium&nbsp;light&nbsp;having&nbsp;lines&nbsp;of wavelength 5890&nbsp;A&nbsp;and 5896&nbsp;A.&nbsp;<\/p>\n<p style=\"position:absolute;top:510px;left:662px;white-space:nowrap\" class=\"ft366\">June&nbsp;<br \/>2012&nbsp;<\/p>\n<p style=\"position:absolute;top:510px;left:725px;white-space:nowrap\" class=\"ft360\">14&nbsp;<\/p>\n<p style=\"position:absolute;top:643px;left:108px;white-space:nowrap\" class=\"ft360\">&nbsp;<\/p>\n<p style=\"position:absolute;top:643px;left:324px;white-space:nowrap\" class=\"ft360\">&nbsp;<\/p>\n<\/div>\n<div id=\"page37-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559037.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft370\">13&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft370\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:404px;white-space:nowrap\" class=\"ft371\"><b>UNIT&nbsp;2\/&nbsp;LECTURE&nbsp;6&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:72px;left:163px;white-space:nowrap\" class=\"ft372\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:115px;left:163px;white-space:nowrap\" class=\"ft373\"><b>NEWTON RINGS&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:115px;left:308px;white-space:nowrap\" class=\"ft371\"><b>[RGPV\/&nbsp;June&nbsp;2013&nbsp;(10)]&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:162px;left:163px;white-space:nowrap\" class=\"ft370\">The&nbsp;phenomenon of&nbsp;Newton&#8217;s&nbsp;rings, named after&nbsp;Isaac&nbsp;Newton who&nbsp;first studied them&nbsp;<\/p>\n<p style=\"position:absolute;top:184px;left:163px;white-space:nowrap\" class=\"ft370\">in&nbsp;1717,&nbsp;is&nbsp;an&nbsp;interference&nbsp;pattern caused by&nbsp;the&nbsp;reflection of&nbsp;light between two&nbsp;<\/p>\n<p style=\"position:absolute;top:206px;left:163px;white-space:nowrap\" class=\"ft370\">surfaces&nbsp;&nbsp;&#8211;&nbsp;&nbsp;a&nbsp;spherical&nbsp;surface&nbsp;and an adjacent flat surface.&nbsp;When viewed&nbsp;with&nbsp;<\/p>\n<p style=\"position:absolute;top:228px;left:163px;white-space:nowrap\" class=\"ft370\">monochromatic&nbsp;light&nbsp;it&nbsp;appears&nbsp;as&nbsp;a series&nbsp;of&nbsp;concentric,&nbsp;alternating&nbsp;bright&nbsp;and&nbsp;dark&nbsp;<\/p>\n<p style=\"position:absolute;top:250px;left:163px;white-space:nowrap\" class=\"ft370\">rings&nbsp;centered at the&nbsp;point of contact between the&nbsp;two&nbsp;surfaces.&nbsp;The&nbsp;light rings&nbsp;are&nbsp;<\/p>\n<p style=\"position:absolute;top:272px;left:163px;white-space:nowrap\" class=\"ft370\">caused by&nbsp;constructive&nbsp;interference&nbsp;between the&nbsp;light rays&nbsp;reflected from&nbsp;both&nbsp;surfaces,&nbsp;<\/p>\n<p style=\"position:absolute;top:294px;left:163px;white-space:nowrap\" class=\"ft370\">while&nbsp;the&nbsp;dark rings&nbsp;are&nbsp;caused by&nbsp;destructive&nbsp;interference<\/p>\n<p style=\"position:absolute;top:294px;left:591px;white-space:nowrap\" class=\"ft372\"><b>.&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:337px;left:163px;white-space:nowrap\" class=\"ft372\"><b>Construction and Theory&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:380px;left:163px;white-space:nowrap\" class=\"ft370\">Rings are&nbsp;fringes of&nbsp;equal&nbsp;thickness.&nbsp;&nbsp;They&nbsp;are&nbsp;observed when light is&nbsp;reflected from&nbsp;a&nbsp;<\/p>\n<p style=\"position:absolute;top:402px;left:163px;white-space:nowrap\" class=\"ft370\">plano-convex&nbsp;lens&nbsp;of a&nbsp;long&nbsp;focal&nbsp;length placed&nbsp;in contact with a&nbsp;plane&nbsp;glass&nbsp;plate.&nbsp;&nbsp;A&nbsp;<\/p>\n<p style=\"position:absolute;top:424px;left:163px;white-space:nowrap\" class=\"ft370\">thin air&nbsp;film&nbsp;is&nbsp;formed&nbsp;between the&nbsp;plate&nbsp;and&nbsp;the&nbsp;lens.&nbsp;&nbsp;&nbsp;The&nbsp;thickness&nbsp;of the&nbsp;air&nbsp;film&nbsp;<\/p>\n<p style=\"position:absolute;top:446px;left:163px;white-space:nowrap\" class=\"ft370\">varies&nbsp;from zero&nbsp;at the&nbsp;point&nbsp;of contact to&nbsp;some&nbsp;value&nbsp;t.&nbsp;&nbsp;&nbsp;If the&nbsp;lens&nbsp;plate&nbsp;system&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:468px;left:163px;white-space:nowrap\" class=\"ft370\">illuminated&nbsp;with&nbsp;monochromatic&nbsp;light&nbsp;falling&nbsp;on&nbsp;it&nbsp;normally,&nbsp;concentric&nbsp;bright&nbsp;and&nbsp;dark&nbsp;<\/p>\n<p style=\"position:absolute;top:490px;left:163px;white-space:nowrap\" class=\"ft370\">interference&nbsp;rings&nbsp;are&nbsp;observed&nbsp;in&nbsp;reflected&nbsp;light.&nbsp;These&nbsp;circular fringes&nbsp;were&nbsp;discovered&nbsp;<\/p>\n<p style=\"position:absolute;top:512px;left:163px;white-space:nowrap\" class=\"ft370\">by&nbsp;Newton and are&nbsp;called Newton&rsquo;s&nbsp;rings.&nbsp;<\/p>\n<p style=\"position:absolute;top:534px;left:163px;white-space:nowrap\" class=\"ft370\">&nbsp;<\/p>\n<p style=\"position:absolute;top:556px;left:163px;white-space:nowrap\" class=\"ft370\">A&nbsp;ray&nbsp;AB&nbsp;incident normally&nbsp;on the&nbsp;system&nbsp;gets&nbsp;partially&nbsp;reflected at the&nbsp;bottom&nbsp;curved&nbsp;<\/p>\n<p style=\"position:absolute;top:578px;left:163px;white-space:nowrap\" class=\"ft370\">surface&nbsp;of&nbsp;the&nbsp;lens&nbsp;(Ray&nbsp;1)&nbsp;and&nbsp;part&nbsp;of&nbsp;the&nbsp;transmitted&nbsp;ray&nbsp;is&nbsp;partially&nbsp;reflected&nbsp;(Ray&nbsp;2)&nbsp;<\/p>\n<p style=\"position:absolute;top:600px;left:163px;white-space:nowrap\" class=\"ft370\">from&nbsp;the&nbsp;top surface&nbsp;of the&nbsp;plane&nbsp;glass&nbsp;plate.&nbsp;&nbsp;The&nbsp;rays&nbsp;1&nbsp;and&nbsp;2&nbsp;are&nbsp;derived&nbsp;from&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:622px;left:163px;white-space:nowrap\" class=\"ft370\">same&nbsp;incident ray&nbsp;by&nbsp;division of amplitude&nbsp;and therefore&nbsp;are&nbsp;coherent.&nbsp;&nbsp;&nbsp;Ray&nbsp;2&nbsp;<\/p>\n<p style=\"position:absolute;top:643px;left:163px;white-space:nowrap\" class=\"ft370\">undergoes&nbsp;a&nbsp;phase&nbsp;change&nbsp;of p&nbsp;upon reflection since&nbsp;it is&nbsp;reflected from&nbsp;air-to-glass&nbsp;<\/p>\n<p style=\"position:absolute;top:666px;left:163px;white-space:nowrap\" class=\"ft370\">boundary.&nbsp;<\/p>\n<p style=\"position:absolute;top:687px;left:163px;white-space:nowrap\" class=\"ft370\">&nbsp;<\/p>\n<p style=\"position:absolute;top:709px;left:163px;white-space:nowrap\" class=\"ft370\">&nbsp;<\/p>\n<p style=\"position:absolute;top:916px;left:623px;white-space:nowrap\" class=\"ft370\">&nbsp;<\/p>\n<p style=\"position:absolute;top:954px;left:163px;white-space:nowrap\" class=\"ft370\">&nbsp;<\/p>\n<p style=\"position:absolute;top:996px;left:163px;white-space:nowrap\" class=\"ft372\"><b>Determination of&nbsp;radius&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:1040px;left:163px;white-space:nowrap\" class=\"ft370\">&nbsp;Let the&nbsp;radius&nbsp;of curvature&nbsp;of the&nbsp;convex&nbsp;lens&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:1039px;left:525px;white-space:nowrap\" class=\"ft372\"><b>R&nbsp;<\/b>and the&nbsp;radius&nbsp;of ring&nbsp;is&nbsp;&#8216;<b>r<\/b>&#8216;. Consider&nbsp;<\/p>\n<p style=\"position:absolute;top:1062px;left:163px;white-space:nowrap\" class=\"ft370\">light of wave&nbsp;length &#8216;<\/p>\n<p style=\"position:absolute;top:1061px;left:317px;white-space:nowrap\" class=\"ft372\"><b>l<\/b>&#8216;&nbsp;falls&nbsp;on&nbsp;the&nbsp;lens.&nbsp;After partial refraction&nbsp;and&nbsp;partial reflection&nbsp;two&nbsp;<\/p>\n<p style=\"position:absolute;top:1084px;left:163px;white-space:nowrap\" class=\"ft370\">rays&nbsp;<\/p>\n<p style=\"position:absolute;top:1083px;left:199px;white-space:nowrap\" class=\"ft372\"><b>1<\/b>&nbsp;and&nbsp;<b>2<\/b>&nbsp;are obtained.&nbsp;These&nbsp;rays&nbsp;interfere each&nbsp;other&nbsp;producing&nbsp;alternate&nbsp;bright&nbsp;<\/p>\n<p style=\"position:absolute;top:1106px;left:163px;white-space:nowrap\" class=\"ft370\">and dark rings.&nbsp;At the&nbsp;point of contact the&nbsp;thickness&nbsp;of air&nbsp;film&nbsp;is&nbsp;zero&nbsp;and the&nbsp;path&nbsp;<\/p>\n<\/div>\n<div id=\"page38-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559038.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft380\">14&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft380\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:163px;white-space:nowrap\" class=\"ft380\">difference&nbsp;is&nbsp;also&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:814px;white-space:nowrap\" class=\"ft380\">&nbsp;<\/p>\n<p style=\"position:absolute;top:68px;left:163px;white-space:nowrap\" class=\"ft380\">zero and&nbsp;as&nbsp;a&nbsp;180<\/p>\n<p style=\"position:absolute;top:66px;left:295px;white-space:nowrap\" class=\"ft381\">O<\/p>\n<p style=\"position:absolute;top:68px;left:303px;white-space:nowrap\" class=\"ft380\">&nbsp;path&nbsp;difference&nbsp;occurs, so&nbsp;they&nbsp;cancel&nbsp;each other&nbsp;and a&nbsp;dark ring&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:90px;left:163px;white-space:nowrap\" class=\"ft380\">obtained at the&nbsp;centre.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:350px;left:605px;white-space:nowrap\" class=\"ft380\">&nbsp;<\/p>\n<p style=\"position:absolute;top:388px;left:163px;white-space:nowrap\" class=\"ft380\">As&nbsp;we&nbsp;move&nbsp;away&nbsp;from&nbsp;the&nbsp;central&nbsp;point ,&nbsp;path&nbsp;difference&nbsp;is&nbsp;also&nbsp;changed and alternate&nbsp;<\/p>\n<p style=\"position:absolute;top:410px;left:163px;white-space:nowrap\" class=\"ft380\">dark and bright rings&nbsp;are&nbsp;obtained.&nbsp;Let us&nbsp;suppose&nbsp;that the&nbsp;thickness&nbsp;of air&nbsp;film&nbsp;is&nbsp;&#8216;<\/p>\n<p style=\"position:absolute;top:410px;left:795px;white-space:nowrap\" class=\"ft382\"><b>t<\/b>&#8216;.&nbsp;<\/p>\n<p style=\"position:absolute;top:432px;left:163px;white-space:nowrap\" class=\"ft380\">By&nbsp;using&nbsp;the&nbsp;theorem&nbsp;of&nbsp;geometry,&nbsp;<\/p>\n<p style=\"position:absolute;top:475px;left:163px;white-space:nowrap\" class=\"ft380\">BD&nbsp;x&nbsp;BE&nbsp;=&nbsp;AB x&nbsp;BC&nbsp;<\/p>\n<p style=\"position:absolute;top:518px;left:163px;white-space:nowrap\" class=\"ft380\">r&nbsp;x r&nbsp;= t&nbsp;(2R-t)&nbsp;<\/p>\n<p style=\"position:absolute;top:561px;left:163px;white-space:nowrap\" class=\"ft380\">r<\/p>\n<p style=\"position:absolute;top:559px;left:170px;white-space:nowrap\" class=\"ft381\">2&nbsp;<\/p>\n<p style=\"position:absolute;top:561px;left:178px;white-space:nowrap\" class=\"ft380\">=<\/p>\n<p style=\"position:absolute;top:561px;left:187px;white-space:nowrap\" class=\"ft382\"><b>&nbsp;<\/b>2Rt&nbsp;&#8211;&nbsp;t<\/p>\n<p style=\"position:absolute;top:559px;left:236px;white-space:nowrap\" class=\"ft383\"><b>2<\/b><\/p>\n<p style=\"position:absolute;top:561px;left:242px;white-space:nowrap\" class=\"ft382\"><b>&nbsp;<\/b>&nbsp;<\/p>\n<p style=\"position:absolute;top:604px;left:163px;white-space:nowrap\" class=\"ft380\">Since&nbsp;t&nbsp;is&nbsp;very&nbsp;small as&nbsp;compared&nbsp;to&nbsp;R&nbsp;,&nbsp;therefore&nbsp;t<\/p>\n<p style=\"position:absolute;top:602px;left:527px;white-space:nowrap\" class=\"ft381\">2<\/p>\n<p style=\"position:absolute;top:604px;left:534px;white-space:nowrap\" class=\"ft380\">&nbsp;should&nbsp;be&nbsp;neglected&nbsp;<\/p>\n<p style=\"position:absolute;top:647px;left:163px;white-space:nowrap\" class=\"ft382\"><b>r<\/b><\/p>\n<p style=\"position:absolute;top:645px;left:170px;white-space:nowrap\" class=\"ft383\"><b>2<\/b><\/p>\n<p style=\"position:absolute;top:647px;left:176px;white-space:nowrap\" class=\"ft382\"><b>&nbsp;= 2Rt&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:690px;left:163px;white-space:nowrap\" class=\"ft380\">In thin films,&nbsp;path difference&nbsp;for&nbsp;constructive&nbsp;interference&nbsp;is:&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:737px;left:492px;white-space:nowrap\" class=\"ft380\">2nt&nbsp;=&nbsp;(m+1\/2)&nbsp;&lambda;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:774px;left:164px;white-space:nowrap\" class=\"ft380\">Where&nbsp;n=&nbsp;refractive&nbsp;index&nbsp;<\/p>\n<p style=\"position:absolute;top:796px;left:164px;white-space:nowrap\" class=\"ft380\">For air n&nbsp;=&nbsp;1&nbsp;<\/p>\n<p style=\"position:absolute;top:818px;left:164px;white-space:nowrap\" class=\"ft380\">Therefore,&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:854px;left:411px;white-space:nowrap\" class=\"ft380\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;2t&nbsp;=&nbsp;(m+1\/2)&nbsp;&lambda;&nbsp; &nbsp; &nbsp;&nbsp;&#8230;&#8230;&#8230;.. (2)&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:892px;left:164px;white-space:nowrap\" class=\"ft380\">For first&nbsp;bright&nbsp;ring&nbsp;m =&nbsp;0&nbsp;<\/p>\n<p style=\"position:absolute;top:914px;left:164px;white-space:nowrap\" class=\"ft380\">For&nbsp;second&nbsp;bright ring&nbsp;m =&nbsp;1&nbsp;<\/p>\n<p style=\"position:absolute;top:936px;left:164px;white-space:nowrap\" class=\"ft380\">For&nbsp;third bright ring&nbsp;m =&nbsp;2&nbsp;<\/p>\n<p style=\"position:absolute;top:958px;left:164px;white-space:nowrap\" class=\"ft384\">Similarly&nbsp;&nbsp;<br \/>For&nbsp;N<\/p>\n<p style=\"position:absolute;top:978px;left:204px;white-space:nowrap\" class=\"ft381\">th<\/p>\n<p style=\"position:absolute;top:989px;left:214px;white-space:nowrap\" class=\"ft380\">&nbsp;bright&nbsp;ring&nbsp;m =&nbsp;N-1&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:1027px;left:164px;white-space:nowrap\" class=\"ft380\">Putting&nbsp;the&nbsp;value&nbsp;of&nbsp;m&nbsp;in equation (2)&nbsp;<\/p>\n<\/div>\n<div id=\"page39-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559039.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft390\">15&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft390\">&nbsp;<\/p>\n<p style=\"position:absolute;top:71px;left:481px;white-space:nowrap\" class=\"ft390\">&nbsp; &nbsp; &nbsp;2t&nbsp;= (N-1+1\/2)&nbsp;&lambda;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:93px;left:500px;white-space:nowrap\" class=\"ft390\">2t&nbsp;= (N-1\/2)&nbsp;&lambda;&nbsp;<\/p>\n<p style=\"position:absolute;top:115px;left:386px;white-space:nowrap\" class=\"ft390\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;t&nbsp;=1\/2 (N-1\/2)&nbsp;&nbsp;&lambda;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&#8230;&#8230;&#8230;&nbsp;(3)&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:166px;left:164px;white-space:nowrap\" class=\"ft390\">Putting&nbsp;the&nbsp;value&nbsp;of &#8216;t&#8217;&nbsp;in equation (1)&nbsp;<\/p>\n<p style=\"position:absolute;top:201px;left:522px;white-space:nowrap\" class=\"ft390\">r<\/p>\n<p style=\"position:absolute;top:190px;left:528px;white-space:nowrap\" class=\"ft391\">2<\/p>\n<p style=\"position:absolute;top:201px;left:534px;white-space:nowrap\" class=\"ft390\">&nbsp;= 2Rt&nbsp;<\/p>\n<p style=\"position:absolute;top:232px;left:471px;white-space:nowrap\" class=\"ft390\">r<\/p>\n<p style=\"position:absolute;top:221px;left:477px;white-space:nowrap\" class=\"ft391\">2<\/p>\n<p style=\"position:absolute;top:232px;left:483px;white-space:nowrap\" class=\"ft390\">&nbsp;=&nbsp;2R&nbsp;.&nbsp;1\/2&nbsp;(N-1\/2)&nbsp;&lambda;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:263px;left:494px;white-space:nowrap\" class=\"ft390\">r<\/p>\n<p style=\"position:absolute;top:252px;left:501px;white-space:nowrap\" class=\"ft391\">2<\/p>\n<p style=\"position:absolute;top:263px;left:507px;white-space:nowrap\" class=\"ft390\">&nbsp;= R (N-1\/2)&nbsp;&lambda;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:306px;left:163px;white-space:nowrap\" class=\"ft390\">&nbsp;<\/p>\n<p style=\"position:absolute;top:349px;left:163px;white-space:nowrap\" class=\"ft392\">&nbsp;<\/p>\n<p style=\"position:absolute;top:371px;left:163px;white-space:nowrap\" class=\"ft392\">&nbsp;<\/p>\n<p style=\"position:absolute;top:393px;left:163px;white-space:nowrap\" class=\"ft392\">Thus&nbsp;the&nbsp;diameters&nbsp;of the&nbsp;bright rings&nbsp;are&nbsp;proportional&nbsp;to&nbsp;the&nbsp;square&nbsp;roots&nbsp;of&nbsp;odd&nbsp;<\/p>\n<p style=\"position:absolute;top:415px;left:163px;white-space:nowrap\" class=\"ft392\">natural&nbsp;numbers&nbsp;<\/p>\n<p style=\"position:absolute;top:437px;left:163px;white-space:nowrap\" class=\"ft392\">as&nbsp;(2N<i>&nbsp;&ndash;<\/i>1)&nbsp;is&nbsp;an odd number.&nbsp;<\/p>\n<p style=\"position:absolute;top:459px;left:163px;white-space:nowrap\" class=\"ft392\">&nbsp;<\/p>\n<p style=\"position:absolute;top:481px;left:163px;white-space:nowrap\" class=\"ft392\">Similarly&nbsp;for a dark&nbsp;ring&nbsp;<\/p>\n<p style=\"position:absolute;top:503px;left:163px;white-space:nowrap\" class=\"ft399\">&nbsp; &nbsp; &nbsp;2t=N&nbsp;&lambda;&nbsp;<br \/>r<\/p>\n<p style=\"position:absolute;top:522px;left:170px;white-space:nowrap\" class=\"ft391\">2<\/p>\n<p style=\"position:absolute;top:534px;left:176px;white-space:nowrap\" class=\"ft390\">&nbsp;=&nbsp;2R&nbsp;N&nbsp;&lambda;&nbsp;<\/p>\n<p style=\"position:absolute;top:556px;left:163px;white-space:nowrap\" class=\"ft390\">&nbsp;<\/p>\n<p style=\"position:absolute;top:578px;left:163px;white-space:nowrap\" class=\"ft392\">&nbsp;<\/p>\n<p style=\"position:absolute;top:600px;left:163px;white-space:nowrap\" class=\"ft392\">or&nbsp;<i>D<\/i><\/p>\n<p style=\"position:absolute;top:597px;left:194px;white-space:nowrap\" class=\"ft394\">2<\/p>\n<p style=\"position:absolute;top:600px;left:200px;white-space:nowrap\" class=\"ft392\">&nbsp;= 4&nbsp;<i>N<\/i><\/p>\n<p style=\"position:absolute;top:600px;left:242px;white-space:nowrap\" class=\"ft390\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:600px;left:255px;white-space:nowrap\" class=\"ft393\"><i>&nbsp;R&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:622px;left:163px;white-space:nowrap\" class=\"ft393\"><i>&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:643px;left:163px;white-space:nowrap\" class=\"ft395\"><i>&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:665px;left:163px;white-space:nowrap\" class=\"ft392\">Thus&nbsp;diameters&nbsp;of dark rings&nbsp;are&nbsp;proportional&nbsp;to&nbsp;the&nbsp;square&nbsp;roots&nbsp;of&nbsp;natural&nbsp;numbers.&nbsp;<\/p>\n<p style=\"position:absolute;top:687px;left:163px;white-space:nowrap\" class=\"ft392\">&nbsp;<\/p>\n<p style=\"position:absolute;top:709px;left:163px;white-space:nowrap\" class=\"ft392\">ITS&nbsp;APPLICATIONS&nbsp;<\/p>\n<p style=\"position:absolute;top:731px;left:163px;white-space:nowrap\" class=\"ft392\">&nbsp;<\/p>\n<p style=\"position:absolute;top:753px;left:190px;white-space:nowrap\" class=\"ft392\">1.&nbsp;&nbsp;Determination of wavelength of light&nbsp;<\/p>\n<p style=\"position:absolute;top:775px;left:163px;white-space:nowrap\" class=\"ft392\">&nbsp;<\/p>\n<p style=\"position:absolute;top:797px;left:163px;white-space:nowrap\" class=\"ft392\">Let D<\/p>\n<p style=\"position:absolute;top:806px;left:201px;white-space:nowrap\" class=\"ft394\">n+p&nbsp;<\/p>\n<p style=\"position:absolute;top:797px;left:222px;white-space:nowrap\" class=\"ft392\">&nbsp;and&nbsp;D<\/p>\n<p style=\"position:absolute;top:806px;left:269px;white-space:nowrap\" class=\"ft394\">n<\/p>\n<p style=\"position:absolute;top:797px;left:275px;white-space:nowrap\" class=\"ft392\">&nbsp;are&nbsp;the&nbsp;diameters&nbsp;of the&nbsp;(n+p)th&nbsp;ring&nbsp;and nth ring, where&nbsp;n &amp;&nbsp;p be&nbsp;<\/p>\n<p style=\"position:absolute;top:819px;left:163px;white-space:nowrap\" class=\"ft392\">integer&nbsp;numbers.&nbsp;then&nbsp;<\/p>\n<p style=\"position:absolute;top:841px;left:163px;white-space:nowrap\" class=\"ft392\">&nbsp;<\/p>\n<p style=\"position:absolute;top:863px;left:420px;white-space:nowrap\" class=\"ft392\">D<\/p>\n<p style=\"position:absolute;top:861px;left:431px;white-space:nowrap\" class=\"ft394\">2<\/p>\n<p style=\"position:absolute;top:872px;left:437px;white-space:nowrap\" class=\"ft394\">n+p&nbsp;<\/p>\n<p style=\"position:absolute;top:863px;left:458px;white-space:nowrap\" class=\"ft392\">&nbsp;=&nbsp;4 (n+p)<\/p>\n<p style=\"position:absolute;top:863px;left:527px;white-space:nowrap\" class=\"ft390\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:863px;left:540px;white-space:nowrap\" class=\"ft392\">&nbsp;R&nbsp;<\/p>\n<p style=\"position:absolute;top:885px;left:163px;white-space:nowrap\" class=\"ft392\">&nbsp;<\/p>\n<p style=\"position:absolute;top:907px;left:442px;white-space:nowrap\" class=\"ft392\">D<\/p>\n<p style=\"position:absolute;top:905px;left:453px;white-space:nowrap\" class=\"ft394\">2<\/p>\n<p style=\"position:absolute;top:916px;left:459px;white-space:nowrap\" class=\"ft394\">n<\/p>\n<p style=\"position:absolute;top:907px;left:465px;white-space:nowrap\" class=\"ft392\">&nbsp;=&nbsp;4&nbsp;<i>n<\/i><\/p>\n<p style=\"position:absolute;top:907px;left:505px;white-space:nowrap\" class=\"ft390\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:907px;left:517px;white-space:nowrap\" class=\"ft393\"><i>&nbsp;R&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:929px;left:163px;white-space:nowrap\" class=\"ft390\">On&nbsp;solving,&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:966px;left:433px;white-space:nowrap\" class=\"ft390\">&lambda;&nbsp;=<\/p>\n<p style=\"position:absolute;top:953px;left:465px;white-space:nowrap\" class=\"ft390\">D<\/p>\n<p style=\"position:absolute;top:961px;left:476px;white-space:nowrap\" class=\"ft396\">n+p<\/p>\n<p style=\"position:absolute;top:951px;left:476px;white-space:nowrap\" class=\"ft396\">2<\/p>\n<p style=\"position:absolute;top:953px;left:502px;white-space:nowrap\" class=\"ft390\">&minus;&nbsp;D<\/p>\n<p style=\"position:absolute;top:961px;left:532px;white-space:nowrap\" class=\"ft396\">n<\/p>\n<p style=\"position:absolute;top:951px;left:532px;white-space:nowrap\" class=\"ft396\">2<\/p>\n<p style=\"position:absolute;top:979px;left:487px;white-space:nowrap\" class=\"ft390\">4pR<\/p>\n<p style=\"position:absolute;top:965px;left:541px;white-space:nowrap\" class=\"ft397\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:998px;left:163px;white-space:nowrap\" class=\"ft397\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:1020px;left:163px;white-space:nowrap\" class=\"ft390\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1043px;left:163px;white-space:nowrap\" class=\"ft390\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1065px;left:163px;white-space:nowrap\" class=\"ft390\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1086px;left:163px;white-space:nowrap\" class=\"ft390\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1108px;left:163px;white-space:nowrap\" class=\"ft390\">&nbsp;<\/p>\n<p style=\"position:absolute;top:316px;left:580px;white-space:nowrap\" class=\"ft390\">)<\/p>\n<p style=\"position:absolute;top:316px;left:571px;white-space:nowrap\" class=\"ft390\">2<\/p>\n<p style=\"position:absolute;top:316px;left:563px;white-space:nowrap\" class=\"ft390\">\/<\/p>\n<p style=\"position:absolute;top:316px;left:552px;white-space:nowrap\" class=\"ft390\">1<\/p>\n<p style=\"position:absolute;top:316px;left:516px;white-space:nowrap\" class=\"ft390\">(<\/p>\n<p style=\"position:absolute;top:310px;left:541px;white-space:nowrap\" class=\"ft390\">&minus;<\/p>\n<p style=\"position:absolute;top:310px;left:466px;white-space:nowrap\" class=\"ft390\">=<\/p>\n<p style=\"position:absolute;top:316px;left:523px;white-space:nowrap\" class=\"ft395\"><i>N<\/i><\/p>\n<p style=\"position:absolute;top:316px;left:494px;white-space:nowrap\" class=\"ft395\"><i>R<\/i><\/p>\n<p style=\"position:absolute;top:316px;left:448px;white-space:nowrap\" class=\"ft395\"><i>r<\/i><\/p>\n<p style=\"position:absolute;top:326px;left:454px;white-space:nowrap\" class=\"ft398\"><i>n<\/i><\/p>\n<p style=\"position:absolute;top:309px;left:505px;white-space:nowrap\" class=\"ft390\">&lambda;<\/p>\n<p style=\"position:absolute;top:355px;left:596px;white-space:nowrap\" class=\"ft390\">)<\/p>\n<p style=\"position:absolute;top:355px;left:587px;white-space:nowrap\" class=\"ft390\">2<\/p>\n<p style=\"position:absolute;top:355px;left:579px;white-space:nowrap\" class=\"ft390\">\/<\/p>\n<p style=\"position:absolute;top:355px;left:568px;white-space:nowrap\" class=\"ft390\">1<\/p>\n<p style=\"position:absolute;top:355px;left:532px;white-space:nowrap\" class=\"ft390\">(<\/p>\n<p style=\"position:absolute;top:355px;left:500px;white-space:nowrap\" class=\"ft390\">2<\/p>\n<p style=\"position:absolute;top:349px;left:557px;white-space:nowrap\" class=\"ft390\">&minus;<\/p>\n<p style=\"position:absolute;top:349px;left:473px;white-space:nowrap\" class=\"ft390\">=<\/p>\n<p style=\"position:absolute;top:355px;left:539px;white-space:nowrap\" class=\"ft395\"><i>N<\/i><\/p>\n<p style=\"position:absolute;top:355px;left:510px;white-space:nowrap\" class=\"ft395\"><i>R<\/i><\/p>\n<p style=\"position:absolute;top:355px;left:449px;white-space:nowrap\" class=\"ft395\"><i>D<\/i><\/p>\n<p style=\"position:absolute;top:365px;left:462px;white-space:nowrap\" class=\"ft398\"><i>n<\/i><\/p>\n<p style=\"position:absolute;top:348px;left:521px;white-space:nowrap\" class=\"ft390\">&lambda;<\/p>\n<p style=\"position:absolute;top:574px;left:261px;white-space:nowrap\" class=\"ft395\"><i>N<\/i><\/p>\n<p style=\"position:absolute;top:574px;left:239px;white-space:nowrap\" class=\"ft395\"><i>R<\/i><\/p>\n<p style=\"position:absolute;top:574px;left:185px;white-space:nowrap\" class=\"ft395\"><i>r<\/i><\/p>\n<p style=\"position:absolute;top:584px;left:191px;white-space:nowrap\" class=\"ft398\"><i>n<\/i><\/p>\n<p style=\"position:absolute;top:567px;left:250px;white-space:nowrap\" class=\"ft390\">&lambda;<\/p>\n<p style=\"position:absolute;top:574px;left:230px;white-space:nowrap\" class=\"ft390\">2<\/p>\n<p style=\"position:absolute;top:568px;left:203px;white-space:nowrap\" class=\"ft390\">=<\/p>\n<p style=\"position:absolute;top:637px;left:261px;white-space:nowrap\" class=\"ft395\"><i>N<\/i><\/p>\n<p style=\"position:absolute;top:637px;left:240px;white-space:nowrap\" class=\"ft395\"><i>R<\/i><\/p>\n<p style=\"position:absolute;top:637px;left:179px;white-space:nowrap\" class=\"ft395\"><i>D<\/i><\/p>\n<p style=\"position:absolute;top:646px;left:192px;white-space:nowrap\" class=\"ft398\"><i>n<\/i><\/p>\n<p style=\"position:absolute;top:630px;left:251px;white-space:nowrap\" class=\"ft390\">&lambda;<\/p>\n<p style=\"position:absolute;top:637px;left:231px;white-space:nowrap\" class=\"ft390\">4<\/p>\n<p style=\"position:absolute;top:631px;left:204px;white-space:nowrap\" class=\"ft390\">=<\/p>\n<\/div>\n<div id=\"page40-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559040.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft400\">16&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:163px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:68px;left:190px;white-space:nowrap\" class=\"ft401\">2.&nbsp;&nbsp;Determination of&nbsp;refractive&nbsp;index&nbsp;of medium&nbsp;<\/p>\n<p style=\"position:absolute;top:90px;left:217px;white-space:nowrap\" class=\"ft401\">&nbsp;<\/p>\n<p style=\"position:absolute;top:112px;left:163px;white-space:nowrap\" class=\"ft401\">Let D<\/p>\n<p style=\"position:absolute;top:120px;left:201px;white-space:nowrap\" class=\"ft402\">n+p&nbsp;<\/p>\n<p style=\"position:absolute;top:112px;left:222px;white-space:nowrap\" class=\"ft401\">&nbsp;and&nbsp;D<\/p>\n<p style=\"position:absolute;top:120px;left:269px;white-space:nowrap\" class=\"ft402\">n<\/p>\n<p style=\"position:absolute;top:112px;left:275px;white-space:nowrap\" class=\"ft401\">&nbsp;are&nbsp;the&nbsp;diameters&nbsp;of the&nbsp;(n+p)th&nbsp;ring&nbsp;and nth ring, where&nbsp;n &amp;&nbsp;p be&nbsp;<\/p>\n<p style=\"position:absolute;top:134px;left:163px;white-space:nowrap\" class=\"ft401\">integer&nbsp;numbers.&nbsp;then&nbsp;<\/p>\n<p style=\"position:absolute;top:156px;left:163px;white-space:nowrap\" class=\"ft401\">for air&nbsp;<\/p>\n<p style=\"position:absolute;top:178px;left:420px;white-space:nowrap\" class=\"ft401\">D<\/p>\n<p style=\"position:absolute;top:176px;left:431px;white-space:nowrap\" class=\"ft402\">2<\/p>\n<p style=\"position:absolute;top:186px;left:437px;white-space:nowrap\" class=\"ft402\">n+p&nbsp;<\/p>\n<p style=\"position:absolute;top:178px;left:458px;white-space:nowrap\" class=\"ft401\">&nbsp;=&nbsp;4 (n+p)<\/p>\n<p style=\"position:absolute;top:178px;left:527px;white-space:nowrap\" class=\"ft400\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:178px;left:540px;white-space:nowrap\" class=\"ft401\">&nbsp;R&nbsp;<\/p>\n<p style=\"position:absolute;top:200px;left:163px;white-space:nowrap\" class=\"ft401\">&nbsp;<\/p>\n<p style=\"position:absolute;top:222px;left:442px;white-space:nowrap\" class=\"ft401\">D<\/p>\n<p style=\"position:absolute;top:220px;left:453px;white-space:nowrap\" class=\"ft402\">2<\/p>\n<p style=\"position:absolute;top:230px;left:459px;white-space:nowrap\" class=\"ft402\">n<\/p>\n<p style=\"position:absolute;top:222px;left:465px;white-space:nowrap\" class=\"ft401\">&nbsp;=&nbsp;4&nbsp;<i>n<\/i><\/p>\n<p style=\"position:absolute;top:222px;left:505px;white-space:nowrap\" class=\"ft400\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:222px;left:517px;white-space:nowrap\" class=\"ft403\"><i>&nbsp;R&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:244px;left:487px;white-space:nowrap\" class=\"ft403\"><i>&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:266px;left:405px;white-space:nowrap\" class=\"ft401\">(D<\/p>\n<p style=\"position:absolute;top:264px;left:421px;white-space:nowrap\" class=\"ft402\">2<\/p>\n<p style=\"position:absolute;top:274px;left:427px;white-space:nowrap\" class=\"ft402\">n+p&nbsp;<\/p>\n<p style=\"position:absolute;top:266px;left:449px;white-space:nowrap\" class=\"ft401\">&nbsp;&#8211;&nbsp;D<\/p>\n<p style=\"position:absolute;top:264px;left:473px;white-space:nowrap\" class=\"ft402\">2<\/p>\n<p style=\"position:absolute;top:274px;left:479px;white-space:nowrap\" class=\"ft402\">n<\/p>\n<p style=\"position:absolute;top:266px;left:486px;white-space:nowrap\" class=\"ft401\">)<\/p>\n<p style=\"position:absolute;top:274px;left:491px;white-space:nowrap\" class=\"ft402\">&nbsp;air<\/p>\n<p style=\"position:absolute;top:266px;left:507px;white-space:nowrap\" class=\"ft401\">=&nbsp;4&nbsp;<i>p<\/i><\/p>\n<p style=\"position:absolute;top:266px;left:542px;white-space:nowrap\" class=\"ft400\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:266px;left:555px;white-space:nowrap\" class=\"ft403\"><i>&nbsp;R&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:288px;left:487px;white-space:nowrap\" class=\"ft403\"><i>&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:310px;left:163px;white-space:nowrap\" class=\"ft401\">For&nbsp;liquid&nbsp;<\/p>\n<p style=\"position:absolute;top:332px;left:398px;white-space:nowrap\" class=\"ft401\">(D<\/p>\n<p style=\"position:absolute;top:330px;left:415px;white-space:nowrap\" class=\"ft402\">2<\/p>\n<p style=\"position:absolute;top:340px;left:421px;white-space:nowrap\" class=\"ft402\">n+p&nbsp;<\/p>\n<p style=\"position:absolute;top:332px;left:442px;white-space:nowrap\" class=\"ft401\">)<\/p>\n<p style=\"position:absolute;top:340px;left:447px;white-space:nowrap\" class=\"ft402\">liq<\/p>\n<p style=\"position:absolute;top:332px;left:459px;white-space:nowrap\" class=\"ft401\">&nbsp;=&nbsp;4 (n+p)<\/p>\n<p style=\"position:absolute;top:332px;left:528px;white-space:nowrap\" class=\"ft400\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:332px;left:541px;white-space:nowrap\" class=\"ft401\">&nbsp;R\/<\/p>\n<p style=\"position:absolute;top:332px;left:562px;white-space:nowrap\" class=\"ft400\">&nbsp;&mu;&nbsp;<\/p>\n<p style=\"position:absolute;top:354px;left:487px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:376px;left:420px;white-space:nowrap\" class=\"ft401\">(D<\/p>\n<p style=\"position:absolute;top:374px;left:437px;white-space:nowrap\" class=\"ft402\">2<\/p>\n<p style=\"position:absolute;top:384px;left:443px;white-space:nowrap\" class=\"ft402\">n<\/p>\n<p style=\"position:absolute;top:376px;left:449px;white-space:nowrap\" class=\"ft401\">)<\/p>\n<p style=\"position:absolute;top:384px;left:455px;white-space:nowrap\" class=\"ft402\">liq<\/p>\n<p style=\"position:absolute;top:376px;left:466px;white-space:nowrap\" class=\"ft401\">&nbsp;=&nbsp;4&nbsp;<i>n<\/i><\/p>\n<p style=\"position:absolute;top:376px;left:506px;white-space:nowrap\" class=\"ft400\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:376px;left:518px;white-space:nowrap\" class=\"ft403\"><i>&nbsp;R\/<\/i><\/p>\n<p style=\"position:absolute;top:376px;left:539px;white-space:nowrap\" class=\"ft400\">&nbsp;&mu;&nbsp;<\/p>\n<p style=\"position:absolute;top:398px;left:487px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:420px;left:393px;white-space:nowrap\" class=\"ft401\">(D<\/p>\n<p style=\"position:absolute;top:417px;left:410px;white-space:nowrap\" class=\"ft402\">2<\/p>\n<p style=\"position:absolute;top:428px;left:416px;white-space:nowrap\" class=\"ft402\">n+p&nbsp;<\/p>\n<p style=\"position:absolute;top:420px;left:437px;white-space:nowrap\" class=\"ft401\">&nbsp;&#8211;&nbsp;D<\/p>\n<p style=\"position:absolute;top:417px;left:462px;white-space:nowrap\" class=\"ft402\">2<\/p>\n<p style=\"position:absolute;top:428px;left:468px;white-space:nowrap\" class=\"ft402\">n<\/p>\n<p style=\"position:absolute;top:420px;left:474px;white-space:nowrap\" class=\"ft401\">)<\/p>\n<p style=\"position:absolute;top:428px;left:480px;white-space:nowrap\" class=\"ft402\">&nbsp;liq&nbsp;<\/p>\n<p style=\"position:absolute;top:420px;left:497px;white-space:nowrap\" class=\"ft401\">=&nbsp;4&nbsp;<i>p<\/i><\/p>\n<p style=\"position:absolute;top:420px;left:533px;white-space:nowrap\" class=\"ft400\">&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:420px;left:545px;white-space:nowrap\" class=\"ft403\"><i>&nbsp;R\/<\/i><\/p>\n<p style=\"position:absolute;top:420px;left:566px;white-space:nowrap\" class=\"ft400\">&nbsp;&mu;&nbsp;<\/p>\n<p style=\"position:absolute;top:442px;left:487px;white-space:nowrap\" class=\"ft403\"><i>&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:464px;left:487px;white-space:nowrap\" class=\"ft403\"><i>&nbsp;<\/i><\/p>\n<p style=\"position:absolute;top:486px;left:163px;white-space:nowrap\" class=\"ft401\">On&nbsp;solving,&nbsp;<\/p>\n<p style=\"position:absolute;top:523px;left:416px;white-space:nowrap\" class=\"ft400\">&micro;&nbsp;=<\/p>\n<p style=\"position:absolute;top:509px;left:449px;white-space:nowrap\" class=\"ft400\">(D<\/p>\n<p style=\"position:absolute;top:518px;left:468px;white-space:nowrap\" class=\"ft404\">n+p<\/p>\n<p style=\"position:absolute;top:507px;left:468px;white-space:nowrap\" class=\"ft404\">2<\/p>\n<p style=\"position:absolute;top:509px;left:494px;white-space:nowrap\" class=\"ft400\">&minus;&nbsp;D<\/p>\n<p style=\"position:absolute;top:518px;left:524px;white-space:nowrap\" class=\"ft404\">n<\/p>\n<p style=\"position:absolute;top:507px;left:524px;white-space:nowrap\" class=\"ft404\">2<\/p>\n<p style=\"position:absolute;top:509px;left:532px;white-space:nowrap\" class=\"ft400\">)<\/p>\n<p style=\"position:absolute;top:518px;left:540px;white-space:nowrap\" class=\"ft404\">air<\/p>\n<p style=\"position:absolute;top:536px;left:449px;white-space:nowrap\" class=\"ft400\">(D<\/p>\n<p style=\"position:absolute;top:545px;left:469px;white-space:nowrap\" class=\"ft404\">n+p<\/p>\n<p style=\"position:absolute;top:534px;left:469px;white-space:nowrap\" class=\"ft404\">2<\/p>\n<p style=\"position:absolute;top:536px;left:495px;white-space:nowrap\" class=\"ft400\">&minus;&nbsp;D<\/p>\n<p style=\"position:absolute;top:545px;left:524px;white-space:nowrap\" class=\"ft404\">n<\/p>\n<p style=\"position:absolute;top:535px;left:524px;white-space:nowrap\" class=\"ft404\">2<\/p>\n<p style=\"position:absolute;top:536px;left:533px;white-space:nowrap\" class=\"ft400\">)<\/p>\n<p style=\"position:absolute;top:545px;left:540px;white-space:nowrap\" class=\"ft404\">liq<\/p>\n<p style=\"position:absolute;top:522px;left:558px;white-space:nowrap\" class=\"ft405\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:558px;left:163px;white-space:nowrap\" class=\"ft401\">&nbsp;<\/p>\n<p style=\"position:absolute;top:580px;left:163px;white-space:nowrap\" class=\"ft401\">&nbsp;<\/p>\n<p style=\"position:absolute;top:603px;left:217px;white-space:nowrap\" class=\"ft406\">&nbsp;<\/p>\n<p style=\"position:absolute;top:623px;left:163px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:645px;left:163px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:667px;left:172px;white-space:nowrap\" class=\"ft400\">S.NO&nbsp;<\/p>\n<p style=\"position:absolute;top:667px;left:319px;white-space:nowrap\" class=\"ft400\">RGPV QUESTION&nbsp;<\/p>\n<p style=\"position:absolute;top:667px;left:565px;white-space:nowrap\" class=\"ft400\">YEAR&nbsp;<\/p>\n<p style=\"position:absolute;top:667px;left:703px;white-space:nowrap\" class=\"ft400\">MARKS&nbsp;<\/p>\n<p style=\"position:absolute;top:690px;left:172px;white-space:nowrap\" class=\"ft400\">Q.1&nbsp;<\/p>\n<p style=\"position:absolute;top:690px;left:249px;white-space:nowrap\" class=\"ft400\">Give&nbsp;details&nbsp;of&nbsp;experimental&nbsp;<\/p>\n<p style=\"position:absolute;top:712px;left:249px;white-space:nowrap\" class=\"ft400\">arrangement to&nbsp;produce&nbsp;Newton&rsquo;s&nbsp;<\/p>\n<p style=\"position:absolute;top:734px;left:249px;white-space:nowrap\" class=\"ft400\">rings&nbsp;by&nbsp;reflected&nbsp;Sodium light.&nbsp;<\/p>\n<p style=\"position:absolute;top:756px;left:249px;white-space:nowrap\" class=\"ft400\">Prove&nbsp;that the&nbsp;diameter&nbsp;of bright&nbsp;<\/p>\n<p style=\"position:absolute;top:778px;left:249px;white-space:nowrap\" class=\"ft400\">fringe&nbsp;is&nbsp;proportional&nbsp;to&nbsp;the&nbsp;square&nbsp;<\/p>\n<p style=\"position:absolute;top:800px;left:249px;white-space:nowrap\" class=\"ft400\">root of add&nbsp;natural&nbsp;numbers.&nbsp;<\/p>\n<p style=\"position:absolute;top:690px;left:547px;white-space:nowrap\" class=\"ft400\">June&nbsp;2013&nbsp;<\/p>\n<p style=\"position:absolute;top:690px;left:720px;white-space:nowrap\" class=\"ft400\">10&nbsp;<\/p>\n<p style=\"position:absolute;top:823px;left:163px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:845px;left:163px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:867px;left:108px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:889px;left:108px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:911px;left:108px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<p style=\"position:absolute;top:933px;left:108px;white-space:nowrap\" class=\"ft400\">&nbsp;<\/p>\n<\/div>\n<div id=\"page41-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559041.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft410\">17&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:159px;white-space:nowrap\" class=\"ft411\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:68px;left:418px;white-space:nowrap\" class=\"ft411\"><b>UNIT-2\/LECTURE 7&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:90px;left:163px;white-space:nowrap\" class=\"ft411\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:112px;left:163px;white-space:nowrap\" class=\"ft411\"><b>Single&nbsp;slit&nbsp;diffraction&nbsp;[RGPV\/&nbsp;Dec2013&nbsp;(7)]&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:134px;left:163px;white-space:nowrap\" class=\"ft411\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:156px;left:163px;white-space:nowrap\" class=\"ft410\">A&nbsp;plane&nbsp;parallel&nbsp;light&nbsp;wave&nbsp;of&nbsp;wavelength&nbsp;&lambda;&nbsp;is&nbsp;incident&nbsp;on&nbsp;a&nbsp;narrow&nbsp;slit&nbsp;of&nbsp;width&nbsp;e&nbsp;after&nbsp;<\/p>\n<p style=\"position:absolute;top:178px;left:163px;white-space:nowrap\" class=\"ft410\">diffraction at slit, the&nbsp;bent rays&nbsp;superimpose&nbsp;to&nbsp;give&nbsp;intensity&nbsp;variation&nbsp;patches&nbsp;on&nbsp;<\/p>\n<p style=\"position:absolute;top:200px;left:163px;white-space:nowrap\" class=\"ft410\">screen known as&nbsp;diffraction pattern.&nbsp;Some&nbsp;light encroaches&nbsp;into&nbsp;the&nbsp;shadow region&nbsp;<\/p>\n<p style=\"position:absolute;top:222px;left:163px;white-space:nowrap\" class=\"ft410\">bound by&nbsp;slit openings.&nbsp;The&nbsp;intensity&nbsp;at the&nbsp;boundary&nbsp;of slit image&nbsp;on&nbsp;the&nbsp;screen has&nbsp;<\/p>\n<p style=\"position:absolute;top:244px;left:163px;white-space:nowrap\" class=\"ft410\">fluctuations&nbsp;called diffraction fringes&nbsp;which can be&nbsp;mathematically&nbsp;investigated.&nbsp;<\/p>\n<p style=\"position:absolute;top:266px;left:159px;white-space:nowrap\" class=\"ft411\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:517px;left:879px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:534px;left:163px;white-space:nowrap\" class=\"ft410\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:556px;left:163px;white-space:nowrap\" class=\"ft410\">In order&nbsp;to&nbsp;find out intensity&nbsp;at p, draw a&nbsp;perpendicular&nbsp;AC&nbsp;on BR, the&nbsp;path difference&nbsp;<\/p>\n<p style=\"position:absolute;top:578px;left:163px;white-space:nowrap\" class=\"ft410\">between&nbsp;secondary&nbsp;wavelets&nbsp;from&nbsp;A&nbsp;and&nbsp;B&nbsp;in&nbsp;direction&nbsp;&theta;&nbsp;<\/p>\n<p style=\"position:absolute;top:600px;left:163px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:600px;left:217px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:600px;left:271px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:600px;left:325px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:622px;left:163px;white-space:nowrap\" class=\"ft410\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;=&nbsp;BC&nbsp;=&nbsp;AB&nbsp;sin&theta;&nbsp;=&nbsp;e&nbsp;sin&theta;&nbsp;<\/p>\n<p style=\"position:absolute;top:644px;left:163px;white-space:nowrap\" class=\"ft410\">Corresponding&nbsp;phase&nbsp;difference&nbsp;<\/p>\n<p style=\"position:absolute;top:666px;left:163px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:688px;left:325px;white-space:nowrap\" class=\"ft410\">=&nbsp;(2&pi;\/&lambda;)&nbsp;.e&nbsp;sin&theta;&nbsp;<\/p>\n<p style=\"position:absolute;top:710px;left:325px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:732px;left:163px;white-space:nowrap\" class=\"ft410\">Let slit is&nbsp;divided in n parts&nbsp;then&nbsp;<\/p>\n<p style=\"position:absolute;top:754px;left:163px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:776px;left:271px;white-space:nowrap\" class=\"ft410\">(1\/n)&nbsp;total&nbsp;phase&nbsp;=&nbsp;(1\/n).&nbsp;(2&pi;\/&lambda;)&nbsp;.e&nbsp;sin&theta;=d&nbsp;<\/p>\n<p style=\"position:absolute;top:798px;left:271px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:820px;left:163px;white-space:nowrap\" class=\"ft410\">Using&nbsp;the&nbsp;method of vector&nbsp;addition&nbsp;of amplitude&nbsp;R&nbsp;is given&nbsp;by&nbsp;<\/p>\n<p style=\"position:absolute;top:842px;left:163px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:869px;left:325px;white-space:nowrap\" class=\"ft410\">R =&nbsp;&#119886;&#119886;<\/p>\n<p style=\"position:absolute;top:864px;left:366px;white-space:nowrap\" class=\"ft412\">sin&nbsp;&#119899;&#119899;&nbsp;&#119889;&#119889;\/2<\/p>\n<p style=\"position:absolute;top:884px;left:371px;white-space:nowrap\" class=\"ft412\">sin&nbsp;&#119889;&#119889;\/2<\/p>\n<p style=\"position:absolute;top:869px;left:420px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:898px;left:325px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:920px;left:325px;white-space:nowrap\" class=\"ft410\">=&nbsp;a sin(&#120587;&#120587;&#120587;&#120587;&nbsp;sin&nbsp;&#120579;&#120579;\/&#120582;&#120582;)\/sin(&pi;&nbsp;&#120587;&#120587;&nbsp;sin&nbsp;&#120579;&#120579;\/&#119899;&#119899;&#120582;&#120582;)&nbsp;<\/p>\n<p style=\"position:absolute;top:941px;left:325px;white-space:nowrap\" class=\"ft413\">&nbsp;<br \/>=&nbsp;&#119886;&#119886;<\/p>\n<p style=\"position:absolute;top:964px;left:359px;white-space:nowrap\" class=\"ft412\">sin&nbsp;&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:984px;left:352px;white-space:nowrap\" class=\"ft412\">sin&nbsp;&#120572;&#120572;\/&#119899;&#119899;<\/p>\n<p style=\"position:absolute;top:968px;left:396px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:997px;left:325px;white-space:nowrap\" class=\"ft413\">&nbsp;<br \/>=&nbsp;&#119886;&#119886;<\/p>\n<p style=\"position:absolute;top:1020px;left:356px;white-space:nowrap\" class=\"ft412\">sin&nbsp;&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:1039px;left:366px;white-space:nowrap\" class=\"ft412\">&#120572;&#120572;\/&#119899;&#119899;<\/p>\n<p style=\"position:absolute;top:1024px;left:389px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1053px;left:325px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1075px;left:325px;white-space:nowrap\" class=\"ft410\">=&nbsp;na&nbsp;(sin&alpha;)\/&alpha;&nbsp;<\/p>\n<p style=\"position:absolute;top:1097px;left:325px;white-space:nowrap\" class=\"ft410\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1119px;left:325px;white-space:nowrap\" class=\"ft410\">=A&nbsp;(sin&alpha;)\/&alpha;&nbsp;<\/p>\n<\/div>\n<div id=\"page42-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559042.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft420\">18&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:155px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<p style=\"position:absolute;top:79px;left:163px;white-space:nowrap\" class=\"ft420\">Thus&nbsp;the&nbsp;resultant amplitude&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:101px;left:163px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<p style=\"position:absolute;top:123px;left:271px;white-space:nowrap\" class=\"ft420\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;R=A&nbsp;(sin&alpha;)\/&alpha;&nbsp;<\/p>\n<p style=\"position:absolute;top:145px;left:271px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<p style=\"position:absolute;top:167px;left:163px;white-space:nowrap\" class=\"ft420\">Now intensity&nbsp;<\/p>\n<p style=\"position:absolute;top:189px;left:271px;white-space:nowrap\" class=\"ft420\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;I=&nbsp;R<\/p>\n<p style=\"position:absolute;top:187px;left:331px;white-space:nowrap\" class=\"ft421\">2&nbsp;<\/p>\n<p style=\"position:absolute;top:189px;left:340px;white-space:nowrap\" class=\"ft420\">= A<\/p>\n<p style=\"position:absolute;top:187px;left:364px;white-space:nowrap\" class=\"ft421\">2<\/p>\n<p style=\"position:absolute;top:189px;left:370px;white-space:nowrap\" class=\"ft420\">&nbsp;[(sin&alpha;)\/&alpha;]<\/p>\n<p style=\"position:absolute;top:187px;left:444px;white-space:nowrap\" class=\"ft421\">2<\/p>\n<p style=\"position:absolute;top:189px;left:450px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<p style=\"position:absolute;top:211px;left:271px;white-space:nowrap\" class=\"ft420\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;I&nbsp;= I<\/p>\n<p style=\"position:absolute;top:219px;left:330px;white-space:nowrap\" class=\"ft421\">o<\/p>\n<p style=\"position:absolute;top:211px;left:336px;white-space:nowrap\" class=\"ft420\">[(sin&alpha;)\/&alpha;]<\/p>\n<p style=\"position:absolute;top:209px;left:406px;white-space:nowrap\" class=\"ft421\">2<\/p>\n<p style=\"position:absolute;top:211px;left:412px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<p style=\"position:absolute;top:233px;left:163px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<p style=\"position:absolute;top:797px;left:792px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1092px;left:791px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1109px;left:163px;white-space:nowrap\" class=\"ft420\">&nbsp;<\/p>\n<\/div>\n<div id=\"page43-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559043.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft430\">19&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:163px;white-space:nowrap\" class=\"ft430\">S.NO&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:299px;white-space:nowrap\" class=\"ft430\">RGPV QUESTION&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:550px;white-space:nowrap\" class=\"ft430\">YEAR&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:706px;white-space:nowrap\" class=\"ft430\">MARKS&nbsp;<\/p>\n<p style=\"position:absolute;top:96px;left:163px;white-space:nowrap\" class=\"ft430\">Q.1&nbsp;<\/p>\n<p style=\"position:absolute;top:96px;left:238px;white-space:nowrap\" class=\"ft430\">Obtain&nbsp;an&nbsp;expression&nbsp;for maxima&nbsp;<\/p>\n<p style=\"position:absolute;top:118px;left:238px;white-space:nowrap\" class=\"ft430\">and minima&nbsp;due&nbsp;to&nbsp;diffraction of&nbsp;<\/p>\n<p style=\"position:absolute;top:140px;left:238px;white-space:nowrap\" class=\"ft430\">light&nbsp;by&nbsp;single&nbsp;slit&nbsp;<\/p>\n<p style=\"position:absolute;top:96px;left:534px;white-space:nowrap\" class=\"ft430\">Dec&nbsp;2013&nbsp;<\/p>\n<p style=\"position:absolute;top:96px;left:728px;white-space:nowrap\" class=\"ft430\">7&nbsp;<\/p>\n<p style=\"position:absolute;top:163px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:185px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:207px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:229px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:251px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:273px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:295px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:317px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:339px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:361px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:383px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:405px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:427px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:449px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:471px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:493px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:515px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:537px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:559px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:580px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:602px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:624px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:646px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:668px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:690px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:712px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:734px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:756px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:778px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:800px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:822px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:844px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:866px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:888px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:910px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:932px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:954px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:976px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:998px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1020px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1042px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1064px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1086px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1108px;left:108px;white-space:nowrap\" class=\"ft430\">&nbsp;<\/p>\n<\/div>\n<div id=\"page44-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559044.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft440\">20&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:487px;white-space:nowrap\" class=\"ft441\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:68px;left:487px;white-space:nowrap\" class=\"ft441\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:90px;left:418px;white-space:nowrap\" class=\"ft441\"><b>UNIT&nbsp;2\/LECTURE 8&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:113px;left:163px;white-space:nowrap\" class=\"ft441\"><b>&nbsp;&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:137px;left:163px;white-space:nowrap\" class=\"ft441\"><b>&nbsp; &nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:134px;left:176px;white-space:nowrap\" class=\"ft442\"><b>DIFFRACTION&nbsp;DUE&nbsp;TO&nbsp;PLANE&nbsp;DIFFRACTION GRATING (OR&nbsp;DIFFRACTION&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:160px;left:163px;white-space:nowrap\" class=\"ft442\"><b>DUE&nbsp;TO A&nbsp;NUMBER&nbsp;OF&nbsp;PARALLEL<\/b><\/p>\n<p style=\"position:absolute;top:163px;left:449px;white-space:nowrap\" class=\"ft441\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:160px;left:453px;white-space:nowrap\" class=\"ft442\"><b>EQUIDISTANT SLITS)&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:186px;left:163px;white-space:nowrap\" class=\"ft441\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:208px;left:163px;white-space:nowrap\" class=\"ft441\"><b>Construction<\/b>.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:230px;left:163px;white-space:nowrap\" class=\"ft440\">A plane&nbsp;transmission&nbsp;grating&nbsp;is&nbsp;constructed&nbsp;by&nbsp;ruling&nbsp;a large&nbsp;number of&nbsp;fine,&nbsp;equidistant&nbsp;<\/p>\n<p style=\"position:absolute;top:252px;left:163px;white-space:nowrap\" class=\"ft440\">and&nbsp;parallel&nbsp;lines&nbsp;on&nbsp;an&nbsp;optically&nbsp;plane&nbsp;glass&nbsp;plate&nbsp;with&nbsp;a diamond&nbsp;p in pen, The&nbsp;ruled&nbsp;<\/p>\n<p style=\"position:absolute;top:274px;left:163px;white-space:nowrap\" class=\"ft440\">portion scatter&nbsp;S&nbsp;the&nbsp;light and thus&nbsp;acts&nbsp;like&nbsp;an opaque&nbsp;region.&nbsp;The&nbsp;unruled portion&nbsp;<\/p>\n<p style=\"position:absolute;top:296px;left:163px;white-space:nowrap\" class=\"ft440\">transmits&nbsp;the&nbsp;light and thus&nbsp;works&nbsp;as&nbsp;transparent region.&nbsp;Thus&nbsp;we&nbsp;get alternate&nbsp;opaque&nbsp;<\/p>\n<p style=\"position:absolute;top:318px;left:163px;white-space:nowrap\" class=\"ft440\">and transparent regions&nbsp;of equal&nbsp;widths&nbsp;and with&nbsp;equal&nbsp;separation.&nbsp;The&nbsp;width of the&nbsp;<\/p>\n<p style=\"position:absolute;top:340px;left:163px;white-space:nowrap\" class=\"ft440\">transparent region becomes&nbsp;comparable&nbsp;to&nbsp;the&nbsp;wavelength of light and&nbsp;therefore&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:362px;left:163px;white-space:nowrap\" class=\"ft440\">diffraction of light takes&nbsp;place.&nbsp;A&nbsp;diffraction grating&nbsp;generally&nbsp;consists&nbsp;of&nbsp;10000&nbsp;to&nbsp;50000&nbsp;<\/p>\n<p style=\"position:absolute;top:384px;left:163px;white-space:nowrap\" class=\"ft440\">lines&nbsp;per&nbsp;inch.&nbsp;<\/p>\n<p style=\"position:absolute;top:406px;left:163px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:427px;left:163px;white-space:nowrap\" class=\"ft441\"><b>Theory:-&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:450px;left:163px;white-space:nowrap\" class=\"ft440\">&nbsp;Thus&nbsp;the&nbsp;diffraction grating&nbsp;is&nbsp;equivalent to&nbsp;N&nbsp;slits&nbsp;arrangement and the&nbsp;diffraction&nbsp;<\/p>\n<p style=\"position:absolute;top:472px;left:163px;white-space:nowrap\" class=\"ft440\">pattern we&nbsp;obtain will&nbsp;be&nbsp;the&nbsp;combined diffraction effect of&nbsp;all&nbsp;such slits.&nbsp;Let&#8217;s&nbsp;e&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:494px;left:163px;white-space:nowrap\" class=\"ft440\">width of each slit and&rsquo;d&rsquo;that of opaque&nbsp;part between them,&nbsp;then (e&nbsp;+&nbsp;d)&nbsp;is&nbsp;known as&nbsp;<\/p>\n<p style=\"position:absolute;top:516px;left:163px;white-space:nowrap\" class=\"ft440\">grating&nbsp;element.&nbsp;The&nbsp;diffracted&nbsp;rays&nbsp;from each&nbsp;of&nbsp;the&nbsp;slits&nbsp;are&nbsp;allowed&nbsp;to&nbsp;fall on&nbsp;a convex&nbsp;<\/p>\n<p style=\"position:absolute;top:538px;left:163px;white-space:nowrap\" class=\"ft440\">lens&nbsp;which focus&nbsp;all&nbsp;of them&nbsp;at a&nbsp;point P&nbsp;on&nbsp;the&nbsp;screen As&nbsp;in the&nbsp;single&nbsp;slit, the&nbsp;waves&nbsp;<\/p>\n<p style=\"position:absolute;top:560px;left:163px;white-space:nowrap\" class=\"ft440\">diffracted&nbsp;from each&nbsp;slit&nbsp;are&nbsp;equivalent&nbsp;to&nbsp;a single&nbsp;wave&nbsp;of&nbsp;amplitude,&nbsp;<\/p>\n<p style=\"position:absolute;top:586px;left:433px;white-space:nowrap\" class=\"ft440\">R =&nbsp;<\/p>\n<p style=\"position:absolute;top:582px;left:460px;white-space:nowrap\" class=\"ft443\">&#119860;&#119860;&nbsp;&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:602px;left:475px;white-space:nowrap\" class=\"ft443\">&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:586px;left:499px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:586px;left:541px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:586px;left:595px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:586px;left:649px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:586px;left:703px;white-space:nowrap\" class=\"ft440\">(1)&nbsp;<\/p>\n<p style=\"position:absolute;top:613px;left:163px;white-space:nowrap\" class=\"ft446\">&nbsp;<br \/>Where&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:640px;left:271px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:640px;left:325px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:640px;left:379px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:640px;left:433px;white-space:nowrap\" class=\"ft440\">&alpha;&nbsp;=&nbsp;<\/p>\n<p style=\"position:absolute;top:635px;left:461px;white-space:nowrap\" class=\"ft443\">&#120587;&#120587;&nbsp;&#120587;&#120587;&nbsp;&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;&#120579;&#120579;<\/p>\n<p style=\"position:absolute;top:655px;left:481px;white-space:nowrap\" class=\"ft443\">&#120582;&#120582;<\/p>\n<p style=\"position:absolute;top:640px;left:510px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:640px;left:541px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:640px;left:595px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:640px;left:649px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:640px;left:703px;white-space:nowrap\" class=\"ft440\">(2)&nbsp;<\/p>\n<p style=\"position:absolute;top:666px;left:163px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:688px;left:163px;white-space:nowrap\" class=\"ft447\">The&nbsp;path&nbsp;difference&nbsp;between&nbsp;any&nbsp;two&nbsp;consecutive&nbsp;waves from&nbsp;two&nbsp;slits&nbsp;(e&nbsp;+&nbsp;d)&nbsp;sin&nbsp;&theta;.&nbsp;<br \/>Therefore, the&nbsp;corresponding&nbsp;phase&nbsp;difference&nbsp;will&nbsp;be<\/p>\n<p style=\"position:absolute;top:710px;left:555px;white-space:nowrap\" class=\"ft443\">2&#120587;&#120587;<\/p>\n<p style=\"position:absolute;top:729px;left:559px;white-space:nowrap\" class=\"ft443\">&#120582;&#120582;<\/p>\n<p style=\"position:absolute;top:714px;left:571px;white-space:nowrap\" class=\"ft440\">(e+&nbsp;d)&nbsp;sin&nbsp;&theta;.&nbsp;Since&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:740px;left:163px;white-space:nowrap\" class=\"ft440\">phasedifference&nbsp;is&nbsp;constant between any&nbsp;two&nbsp;consecutive&nbsp;waves&nbsp;it&nbsp;can&nbsp;be&nbsp;taken&nbsp;as&nbsp;<\/p>\n<p style=\"position:absolute;top:762px;left:163px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:784px;left:379px;white-space:nowrap\" class=\"ft443\">2&#120587;&#120587;<\/p>\n<p style=\"position:absolute;top:804px;left:384px;white-space:nowrap\" class=\"ft443\">&#120582;&#120582;<\/p>\n<p style=\"position:absolute;top:788px;left:395px;white-space:nowrap\" class=\"ft440\">(e+&nbsp;d)&nbsp;sin&nbsp;&theta;&nbsp;=&nbsp;2&beta;&nbsp;<\/p>\n<p style=\"position:absolute;top:788px;left:541px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:788px;left:595px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:788px;left:649px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:788px;left:703px;white-space:nowrap\" class=\"ft440\">(3)&nbsp;<\/p>\n<p style=\"position:absolute;top:815px;left:163px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:837px;left:163px;white-space:nowrap\" class=\"ft447\">Thus&nbsp;we&nbsp;have&nbsp;to&nbsp;find&nbsp;out&nbsp;the&nbsp;resultant&nbsp;of&nbsp;N&nbsp;vibrations&nbsp;in&nbsp;a&nbsp;direction&nbsp;&theta;&nbsp;and&nbsp;each&nbsp;vibration&nbsp;<br \/>is&nbsp;of&nbsp;amplitude<\/p>\n<p style=\"position:absolute;top:859px;left:272px;white-space:nowrap\" class=\"ft443\">&#119860;&#119860;&nbsp;&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:879px;left:287px;white-space:nowrap\" class=\"ft443\">&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:864px;left:311px;white-space:nowrap\" class=\"ft440\">&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:890px;left:163px;white-space:nowrap\" class=\"ft440\">Similar to&nbsp;the&nbsp;resultant&nbsp;of&nbsp;n-harmonic&nbsp;waves, the&nbsp;resultant of N&nbsp;slits&nbsp;may&nbsp;be&nbsp;given&nbsp;as,&nbsp;<\/p>\n<p style=\"position:absolute;top:912px;left:163px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:948px;left:325px;white-space:nowrap\" class=\"ft440\">R&rsquo;&nbsp;=&nbsp;<\/p>\n<p style=\"position:absolute;top:941px;left:357px;white-space:nowrap\" class=\"ft443\">&#119877;&#119877;&nbsp;sin<\/p>\n<p style=\"position:absolute;top:935px;left:386px;white-space:nowrap\" class=\"ft444\">2&nbsp;&#119873;&#119873;&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:949px;left:397px;white-space:nowrap\" class=\"ft444\">2<\/p>\n<p style=\"position:absolute;top:966px;left:369px;white-space:nowrap\" class=\"ft443\">sin<\/p>\n<p style=\"position:absolute;top:960px;left:387px;white-space:nowrap\" class=\"ft444\">2&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:974px;left:391px;white-space:nowrap\" class=\"ft444\">2<\/p>\n<p style=\"position:absolute;top:948px;left:414px;white-space:nowrap\" class=\"ft440\">&nbsp;=&nbsp;<\/p>\n<p style=\"position:absolute;top:943px;left:431px;white-space:nowrap\" class=\"ft443\">&#119877;&#119877;&nbsp;sin&nbsp;&#119873;&#119873;&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:963px;left:442px;white-space:nowrap\" class=\"ft443\">sin&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:948px;left:484px;white-space:nowrap\" class=\"ft440\">&nbsp;=<\/p>\n<p style=\"position:absolute;top:943px;left:497px;white-space:nowrap\" class=\"ft443\">&#119860;&#119860;&nbsp;&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:963px;left:512px;white-space:nowrap\" class=\"ft443\">&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:943px;left:539px;white-space:nowrap\" class=\"ft443\">sin&nbsp;&#119873;&#119873;&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:963px;left:545px;white-space:nowrap\" class=\"ft443\">sin&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:948px;left:581px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:983px;left:163px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1005px;left:163px;white-space:nowrap\" class=\"ft440\">Thus&nbsp;the&nbsp;resultant intensity&nbsp;at P&nbsp;may&nbsp;be&nbsp;given as,&nbsp;<\/p>\n<p style=\"position:absolute;top:1027px;left:163px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1056px;left:325px;white-space:nowrap\" class=\"ft440\">I&nbsp;= R&rsquo;<\/p>\n<p style=\"position:absolute;top:1054px;left:361px;white-space:nowrap\" class=\"ft445\">2<\/p>\n<p style=\"position:absolute;top:1056px;left:367px;white-space:nowrap\" class=\"ft440\">=&nbsp;<\/p>\n<p style=\"position:absolute;top:1052px;left:380px;white-space:nowrap\" class=\"ft443\">&#119860;&#119860;<\/p>\n<p style=\"position:absolute;top:1049px;left:389px;white-space:nowrap\" class=\"ft444\">2<\/p>\n<p style=\"position:absolute;top:1052px;left:395px;white-space:nowrap\" class=\"ft443\">&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;<\/p>\n<p style=\"position:absolute;top:1049px;left:415px;white-space:nowrap\" class=\"ft444\">2<\/p>\n<p style=\"position:absolute;top:1052px;left:421px;white-space:nowrap\" class=\"ft443\">&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:1071px;left:397px;white-space:nowrap\" class=\"ft443\">&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:1070px;left:406px;white-space:nowrap\" class=\"ft444\">2<\/p>\n<p style=\"position:absolute;top:1052px;left:433px;white-space:nowrap\" class=\"ft443\">&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;<\/p>\n<p style=\"position:absolute;top:1049px;left:452px;white-space:nowrap\" class=\"ft444\">2<\/p>\n<p style=\"position:absolute;top:1052px;left:461px;white-space:nowrap\" class=\"ft443\">&#119873;&#119873;&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:1071px;left:440px;white-space:nowrap\" class=\"ft443\">&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;<\/p>\n<p style=\"position:absolute;top:1070px;left:459px;white-space:nowrap\" class=\"ft444\">2<\/p>\n<p style=\"position:absolute;top:1071px;left:468px;white-space:nowrap\" class=\"ft443\">&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:1056px;left:483px;white-space:nowrap\" class=\"ft440\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:1056px;left:541px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1056px;left:595px;white-space:nowrap\" class=\"ft440\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1056px;left:649px;white-space:nowrap\" class=\"ft440\">(4)&nbsp;<\/p>\n<p style=\"position:absolute;top:1085px;left:163px;white-space:nowrap\" class=\"ft441\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:1106px;left:163px;white-space:nowrap\" class=\"ft441\"><b>&nbsp;<\/b><\/p>\n<\/div>\n<div id=\"page45-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559045.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft450\">21&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:163px;white-space:nowrap\" class=\"ft451\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:68px;left:163px;white-space:nowrap\" class=\"ft451\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:90px;left:163px;white-space:nowrap\" class=\"ft455\"><b>&nbsp;<br \/><\/b>Here the factor&nbsp;<\/p>\n<p style=\"position:absolute;top:115px;left:278px;white-space:nowrap\" class=\"ft452\">&#119860;&#119860;<\/p>\n<p style=\"position:absolute;top:112px;left:286px;white-space:nowrap\" class=\"ft453\">2<\/p>\n<p style=\"position:absolute;top:115px;left:293px;white-space:nowrap\" class=\"ft452\">&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;<\/p>\n<p style=\"position:absolute;top:112px;left:312px;white-space:nowrap\" class=\"ft453\">2<\/p>\n<p style=\"position:absolute;top:115px;left:319px;white-space:nowrap\" class=\"ft452\">&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:134px;left:295px;white-space:nowrap\" class=\"ft452\">&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:133px;left:304px;white-space:nowrap\" class=\"ft453\">2<\/p>\n<p style=\"position:absolute;top:119px;left:328px;white-space:nowrap\" class=\"ft450\">&nbsp;is&nbsp;the&nbsp;intensity&nbsp;factor due&nbsp;to&nbsp;a single&nbsp;slit&nbsp;while<\/p>\n<p style=\"position:absolute;top:115px;left:665px;white-space:nowrap\" class=\"ft452\">&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;<\/p>\n<p style=\"position:absolute;top:112px;left:684px;white-space:nowrap\" class=\"ft453\">2<\/p>\n<p style=\"position:absolute;top:115px;left:693px;white-space:nowrap\" class=\"ft452\">&#119873;&#119873;&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:134px;left:672px;white-space:nowrap\" class=\"ft452\">&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;<\/p>\n<p style=\"position:absolute;top:133px;left:691px;white-space:nowrap\" class=\"ft453\">2<\/p>\n<p style=\"position:absolute;top:134px;left:700px;white-space:nowrap\" class=\"ft452\">&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:119px;left:715px;white-space:nowrap\" class=\"ft450\">due&nbsp;to&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:148px;left:163px;white-space:nowrap\" class=\"ft450\">interference&nbsp;from all the&nbsp;N&nbsp;slits.&nbsp;<\/p>\n<p style=\"position:absolute;top:170px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:192px;left:163px;white-space:nowrap\" class=\"ft450\">Principal maxima.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:214px;left:163px;white-space:nowrap\" class=\"ft450\">For maximum intensity,&nbsp;we&nbsp;have,&nbsp;<\/p>\n<p style=\"position:absolute;top:236px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:258px;left:325px;white-space:nowrap\" class=\"ft450\">sin&beta; =&nbsp;0&nbsp;<\/p>\n<p style=\"position:absolute;top:258px;left:433px;white-space:nowrap\" class=\"ft450\">or&nbsp;<\/p>\n<p style=\"position:absolute;top:258px;left:487px;white-space:nowrap\" class=\"ft450\">&beta; =&nbsp;+_&nbsp;n&pi;,&nbsp;<\/p>\n<p style=\"position:absolute;top:258px;left:595px;white-space:nowrap\" class=\"ft450\">n&nbsp;=&nbsp;0,1,2,&hellip;&hellip;&nbsp;<\/p>\n<p style=\"position:absolute;top:280px;left:163px;white-space:nowrap\" class=\"ft456\">&nbsp;<br \/>But in this&nbsp;condition<\/p>\n<p style=\"position:absolute;top:303px;left:310px;white-space:nowrap\" class=\"ft452\">sin&nbsp;&#119873;&#119873;&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:322px;left:317px;white-space:nowrap\" class=\"ft452\">sin&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:307px;left:353px;white-space:nowrap\" class=\"ft450\">=&nbsp;<\/p>\n<p style=\"position:absolute;top:303px;left:366px;white-space:nowrap\" class=\"ft457\">0<br \/>0<\/p>\n<p style=\"position:absolute;top:307px;left:373px;white-space:nowrap\" class=\"ft450\">is&nbsp;in indeterminate&nbsp;form.&nbsp;Thus&nbsp;to&nbsp;find&nbsp;its&nbsp;value&nbsp;we&nbsp;have&nbsp;to&nbsp;<\/p>\n<p style=\"position:absolute;top:336px;left:163px;white-space:nowrap\" class=\"ft450\">adopt the&nbsp;differential&nbsp;calculus&nbsp;procedure, according&nbsp;to&nbsp;which,&nbsp;<\/p>\n<p style=\"position:absolute;top:358px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:397px;left:325px;white-space:nowrap\" class=\"ft450\">lim<\/p>\n<p style=\"position:absolute;top:406px;left:349px;white-space:nowrap\" class=\"ft452\">&#120573;&#120573;&rarr;&plusmn;&#119899;&#119899;&#120587;&#120587;<\/p>\n<p style=\"position:absolute;top:391px;left:399px;white-space:nowrap\" class=\"ft452\">sin&nbsp;&#119873;&#119873;&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:411px;left:406px;white-space:nowrap\" class=\"ft452\">sin&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:396px;left:442px;white-space:nowrap\" class=\"ft450\">&nbsp;=&nbsp;lim<\/p>\n<p style=\"position:absolute;top:406px;left:483px;white-space:nowrap\" class=\"ft452\">&#120573;&#120573;&rarr;&plusmn;&#119899;&#119899;&#120587;&#120587;<\/p>\n<p style=\"position:absolute;top:381px;left:537px;white-space:nowrap\" class=\"ft453\">&#119889;&#119889;<\/p>\n<p style=\"position:absolute;top:395px;left:533px;white-space:nowrap\" class=\"ft453\">&#119889;&#119889;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:386px;left:548px;white-space:nowrap\" class=\"ft452\">sin&nbsp;&#119873;&#119873;&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:408px;left:542px;white-space:nowrap\" class=\"ft453\">&#119889;&#119889;<\/p>\n<p style=\"position:absolute;top:422px;left:538px;white-space:nowrap\" class=\"ft453\">&#119889;&#119889;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:413px;left:555px;white-space:nowrap\" class=\"ft452\">sin&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:396px;left:590px;white-space:nowrap\" class=\"ft450\">&nbsp;=&nbsp;&nbsp;lim<\/p>\n<p style=\"position:absolute;top:413px;left:607px;white-space:nowrap\" class=\"ft452\">&#120573;&#120573;&rarr;&plusmn;&#119899;&#119899;&#120587;&#120587;<\/p>\n<p style=\"position:absolute;top:391px;left:657px;white-space:nowrap\" class=\"ft452\">&#119873;&#119873;&nbsp;cos&nbsp;&#119873;&#119873;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:411px;left:668px;white-space:nowrap\" class=\"ft452\">cos&nbsp;&#120573;&#120573;<\/p>\n<p style=\"position:absolute;top:396px;left:710px;white-space:nowrap\" class=\"ft450\">&nbsp;= N&nbsp;<\/p>\n<p style=\"position:absolute;top:433px;left:163px;white-space:nowrap\" class=\"ft458\">&nbsp;<br \/>Thus,&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:462px;left:271px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:462px;left:325px;white-space:nowrap\" class=\"ft450\">I =&nbsp;<\/p>\n<p style=\"position:absolute;top:457px;left:347px;white-space:nowrap\" class=\"ft452\">&#119860;&#119860;<\/p>\n<p style=\"position:absolute;top:455px;left:355px;white-space:nowrap\" class=\"ft453\">2<\/p>\n<p style=\"position:absolute;top:457px;left:362px;white-space:nowrap\" class=\"ft452\">&#119904;&#119904;&#119904;&#119904;&#119899;&#119899;<\/p>\n<p style=\"position:absolute;top:455px;left:381px;white-space:nowrap\" class=\"ft453\">2<\/p>\n<p style=\"position:absolute;top:457px;left:388px;white-space:nowrap\" class=\"ft452\">&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:477px;left:364px;white-space:nowrap\" class=\"ft452\">&#120572;&#120572;<\/p>\n<p style=\"position:absolute;top:475px;left:373px;white-space:nowrap\" class=\"ft453\">2<\/p>\n<p style=\"position:absolute;top:462px;left:397px;white-space:nowrap\" class=\"ft450\">&nbsp;N<\/p>\n<p style=\"position:absolute;top:460px;left:412px;white-space:nowrap\" class=\"ft454\">2<\/p>\n<p style=\"position:absolute;top:462px;left:419px;white-space:nowrap\" class=\"ft450\">&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:462px;left:487px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:462px;left:541px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:462px;left:595px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:462px;left:649px;white-space:nowrap\" class=\"ft450\">(5)&nbsp;<\/p>\n<p style=\"position:absolute;top:462px;left:703px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:488px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:488px;left:217px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:510px;left:163px;white-space:nowrap\" class=\"ft450\">The&nbsp;intensity&nbsp;at&nbsp;these&nbsp;maxima is&nbsp;maximum and&nbsp;that&nbsp;is&nbsp;why&nbsp;it&nbsp;is&nbsp;principle&nbsp;maxima.&nbsp;<\/p>\n<p style=\"position:absolute;top:532px;left:163px;white-space:nowrap\" class=\"ft450\">Therefore,&nbsp;the&nbsp;condition&nbsp;for principal maxima is&nbsp;<\/p>\n<p style=\"position:absolute;top:554px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:576px;left:325px;white-space:nowrap\" class=\"ft450\">sin&nbsp;&beta; =&nbsp;0&nbsp;<\/p>\n<p style=\"position:absolute;top:576px;left:433px;white-space:nowrap\" class=\"ft450\">or&nbsp;<\/p>\n<p style=\"position:absolute;top:576px;left:487px;white-space:nowrap\" class=\"ft450\">&beta; =&nbsp;&plusmn;&nbsp;n&pi;&nbsp;<\/p>\n<p style=\"position:absolute;top:600px;left:163px;white-space:nowrap\" class=\"ft450\">or&nbsp;<\/p>\n<p style=\"position:absolute;top:600px;left:217px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:600px;left:271px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:596px;left:325px;white-space:nowrap\" class=\"ft452\">&#120587;&#120587;<\/p>\n<p style=\"position:absolute;top:616px;left:326px;white-space:nowrap\" class=\"ft452\">&#120582;&#120582;<\/p>\n<p style=\"position:absolute;top:600px;left:334px;white-space:nowrap\" class=\"ft450\">(e+&nbsp;d)&nbsp;sin&nbsp;&theta;&nbsp;=&nbsp;&plusmn;&nbsp;n&pi;&nbsp;<\/p>\n<p style=\"position:absolute;top:626px;left:163px;white-space:nowrap\" class=\"ft450\">or&nbsp;<\/p>\n<p style=\"position:absolute;top:626px;left:217px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:626px;left:271px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:626px;left:325px;white-space:nowrap\" class=\"ft450\">(e+&nbsp;d)&nbsp;sin&nbsp;&theta;&nbsp;=&nbsp;&plusmn;&nbsp;n&lambda;&nbsp;<\/p>\n<p style=\"position:absolute;top:626px;left:487px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:626px;left:541px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:626px;left:595px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:626px;left:649px;white-space:nowrap\" class=\"ft450\">(6)&nbsp;<\/p>\n<p style=\"position:absolute;top:648px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:670px;left:163px;white-space:nowrap\" class=\"ft450\">For&nbsp;n=0,&nbsp;we&nbsp;get&nbsp;&theta;&nbsp;=&nbsp;0,&nbsp;which&nbsp;gives the&nbsp;direction of the&nbsp;zero&nbsp;order&nbsp;principal&nbsp;maximum.&nbsp;<\/p>\n<p style=\"position:absolute;top:692px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:714px;left:163px;white-space:nowrap\" class=\"ft450\">The&nbsp;values&nbsp;n=1, 2, 3&hellip;.&nbsp;correspond to&nbsp;the&nbsp;first, second, third&hellip;..order&nbsp;principal&nbsp;maxima.&nbsp;<\/p>\n<p style=\"position:absolute;top:736px;left:163px;white-space:nowrap\" class=\"ft450\">Here&nbsp;the&nbsp;sign shows&nbsp;that the&nbsp;two&nbsp;principal&nbsp;maxima&nbsp;of the&nbsp;same&nbsp;order&nbsp;lie&nbsp;on either&nbsp;side&nbsp;<\/p>\n<p style=\"position:absolute;top:758px;left:163px;white-space:nowrap\" class=\"ft450\">of&nbsp;zero&nbsp;order maximum.&nbsp;<\/p>\n<p style=\"position:absolute;top:780px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:802px;left:163px;white-space:nowrap\" class=\"ft450\">Minima.&nbsp;<\/p>\n<p style=\"position:absolute;top:824px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:846px;left:163px;white-space:nowrap\" class=\"ft450\">For&nbsp;sin&nbsp;N&nbsp;&beta; =&nbsp;0.But&nbsp;sin&nbsp;&beta;&nbsp;&ne;&nbsp;0&nbsp;<\/p>\n<p style=\"position:absolute;top:868px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:890px;left:163px;white-space:nowrap\" class=\"ft450\">We&nbsp;get&nbsp;the&nbsp;minimum intensity.&nbsp;A series&nbsp;of&nbsp;minima,&nbsp;thus,&nbsp;obtained&nbsp;for&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:912px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:934px;left:379px;white-space:nowrap\" class=\"ft450\">N&beta; =&nbsp;&plusmn;&nbsp;m&pi;&nbsp;<\/p>\n<p style=\"position:absolute;top:958px;left:163px;white-space:nowrap\" class=\"ft450\">or&nbsp;<\/p>\n<p style=\"position:absolute;top:958px;left:217px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:958px;left:271px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:958px;left:325px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:958px;left:379px;white-space:nowrap\" class=\"ft450\">N<\/p>\n<p style=\"position:absolute;top:954px;left:391px;white-space:nowrap\" class=\"ft452\">&#120587;&#120587;<\/p>\n<p style=\"position:absolute;top:974px;left:391px;white-space:nowrap\" class=\"ft452\">&#120582;&#120582;<\/p>\n<p style=\"position:absolute;top:958px;left:400px;white-space:nowrap\" class=\"ft450\">(e+&nbsp;d)&nbsp;sin&nbsp;&theta;&nbsp;=&nbsp;&plusmn;&nbsp;m&pi;&nbsp;<\/p>\n<p style=\"position:absolute;top:985px;left:163px;white-space:nowrap\" class=\"ft450\">or&nbsp;<\/p>\n<p style=\"position:absolute;top:985px;left:217px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:985px;left:271px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:985px;left:325px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:985px;left:379px;white-space:nowrap\" class=\"ft450\">N (e+&nbsp;d)&nbsp;sin&nbsp;&theta;&nbsp;=&nbsp;&plusmn;m&lambda;&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:985px;left:595px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:985px;left:649px;white-space:nowrap\" class=\"ft450\">(7)&nbsp;<\/p>\n<p style=\"position:absolute;top:1007px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1029px;left:163px;white-space:nowrap\" class=\"ft450\">Thus&nbsp;for all integral values&nbsp;of&nbsp;m except&nbsp;0,&nbsp;N,&nbsp;2N,&nbsp;3N,&hellip;..we&nbsp;get&nbsp;a minima,&nbsp;because&nbsp;for m=&nbsp;<\/p>\n<p style=\"position:absolute;top:1051px;left:163px;white-space:nowrap\" class=\"ft450\">O,&nbsp;N,&nbsp;2N,&nbsp;3N,&hellip;..the&nbsp;value&nbsp;of&nbsp;sin&nbsp;P&nbsp;=&nbsp;0&nbsp;and&nbsp;this&nbsp;will give&nbsp;the&nbsp;positions&nbsp;of&nbsp;principal maxima.&nbsp;<\/p>\n<p style=\"position:absolute;top:1073px;left:163px;white-space:nowrap\" class=\"ft450\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1094px;left:163px;white-space:nowrap\" class=\"ft451\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:1116px;left:163px;white-space:nowrap\" class=\"ft451\"><b>&nbsp;<\/b><\/p>\n<\/div>\n<div id=\"page46-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559046.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft460\">22&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:163px;white-space:nowrap\" class=\"ft461\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:68px;left:418px;white-space:nowrap\" class=\"ft461\"><b>UNIT&nbsp;2\/LECTURE 9&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:90px;left:163px;white-space:nowrap\" class=\"ft461\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:112px;left:163px;white-space:nowrap\" class=\"ft461\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:134px;left:163px;white-space:nowrap\" class=\"ft461\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:156px;left:163px;white-space:nowrap\" class=\"ft461\"><b>RESOLVING POWER&nbsp;OF&nbsp;PLANE&nbsp;DIFFRACTION&nbsp;GRATING&nbsp;[RGPV\/&nbsp;Dec2012 (10)]&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:178px;left:163px;white-space:nowrap\" class=\"ft461\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:200px;left:163px;white-space:nowrap\" class=\"ft460\">The&nbsp;resolving&nbsp;power&nbsp;of a&nbsp;grating&nbsp;is&nbsp;defined as&nbsp;the&nbsp;ratio&nbsp;of&nbsp;the&nbsp;wavelength of any&nbsp;spectral&nbsp;<\/p>\n<p style=\"position:absolute;top:222px;left:163px;white-space:nowrap\" class=\"ft460\">line&nbsp;to&nbsp;the&nbsp;difference&nbsp;in wavelength between this&nbsp;line&nbsp;and a&nbsp;neighbouring&nbsp;line&nbsp;such that&nbsp;<\/p>\n<p style=\"position:absolute;top:244px;left:163px;white-space:nowrap\" class=\"ft460\">two&nbsp;lines&nbsp;appear&nbsp;to&nbsp;be&nbsp;just resolved.&nbsp;<\/p>\n<p style=\"position:absolute;top:587px;left:805px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:604px;left:163px;white-space:nowrap\" class=\"ft460\">In above&nbsp;figure, XY&nbsp;is&nbsp;a&nbsp;grating&nbsp;surface&nbsp;and MN&nbsp;is&nbsp;the&nbsp;field of view of the&nbsp;telescope.P1&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:626px;left:163px;white-space:nowrap\" class=\"ft460\">the&nbsp;nth&nbsp;primary&nbsp;maximum of&nbsp;a spectral line&nbsp;of&nbsp;wavelength&nbsp;&lambda;&nbsp;at an angle&nbsp;of diffraction&nbsp;&theta;n&nbsp;<\/p>\n<p style=\"position:absolute;top:648px;left:163px;white-space:nowrap\" class=\"ft460\">.&nbsp;P2&nbsp;is&nbsp;the&nbsp;nth primary&nbsp;maximum&nbsp;of a&nbsp;second spectral&nbsp;line&nbsp;of wavelength&nbsp;&lambda;&nbsp;+d&lambda;&nbsp;at&nbsp;a&nbsp;<\/p>\n<p style=\"position:absolute;top:670px;left:163px;white-space:nowrap\" class=\"ft460\">diffracting&nbsp;angle&nbsp;of&nbsp;&theta;n+d&theta;.P1&nbsp;and P2&nbsp;are&nbsp;the&nbsp;spectral&nbsp;lines&nbsp;in the&nbsp;nth order.&nbsp;<\/p>\n<p style=\"position:absolute;top:692px;left:163px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:714px;left:163px;white-space:nowrap\" class=\"ft460\">The&nbsp;direction of nth&nbsp;primary&nbsp;maximum&nbsp;for&nbsp;a&nbsp;wavelength&nbsp;&lambda;&nbsp;is given&nbsp;by&nbsp;<\/p>\n<p style=\"position:absolute;top:736px;left:163px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:758px;left:271px;white-space:nowrap\" class=\"ft460\">(a&nbsp;+ b) sin&nbsp;&theta;n =&nbsp;n&nbsp;&lambda;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:758px;left:487px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:758px;left:541px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:758px;left:595px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:758px;left:649px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:758px;left:703px;white-space:nowrap\" class=\"ft460\">(i)&nbsp;<\/p>\n<p style=\"position:absolute;top:780px;left:271px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:802px;left:163px;white-space:nowrap\" class=\"ft460\">The&nbsp;direction&nbsp;of&nbsp;nth&nbsp;primary&nbsp;maximum for a wavelength&nbsp;(&lambda;+d&lambda;)&nbsp;is given&nbsp;by&nbsp;<\/p>\n<p style=\"position:absolute;top:824px;left:163px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:846px;left:271px;white-space:nowrap\" class=\"ft460\">(a&nbsp;+ b) sin(&theta;n+d&theta;) = n&nbsp;(&lambda;+d&lambda;)&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:846px;left:541px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:846px;left:595px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:846px;left:649px;white-space:nowrap\" class=\"ft460\">(ii)&nbsp;<\/p>\n<p style=\"position:absolute;top:868px;left:271px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:890px;left:163px;white-space:nowrap\" class=\"ft460\">The&nbsp;two&nbsp;lines&nbsp;will&nbsp;appear&nbsp;just resolved if the&nbsp;angle&nbsp;of diffraction (&theta;n +&nbsp;d&theta;)&nbsp;also&nbsp;<\/p>\n<p style=\"position:absolute;top:912px;left:163px;white-space:nowrap\" class=\"ft460\">corresponds&nbsp;to&nbsp;the&nbsp;direction of the&nbsp;first secondary&nbsp;minimum&nbsp;after&nbsp;the&nbsp;nth primary&nbsp;<\/p>\n<p style=\"position:absolute;top:934px;left:163px;white-space:nowrap\" class=\"ft460\">maximum&nbsp;at&nbsp;P1.&nbsp;This&nbsp;is&nbsp;possible&nbsp;if the&nbsp;extra&nbsp;path&nbsp;difference&nbsp;introduced is&nbsp;&lambda;&nbsp;\/N&nbsp;where&nbsp;N&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:956px;left:163px;white-space:nowrap\" class=\"ft460\">the&nbsp;total&nbsp;number&nbsp;of lines&nbsp;of the&nbsp;grating&nbsp;surface.&nbsp;<\/p>\n<p style=\"position:absolute;top:978px;left:163px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1000px;left:163px;white-space:nowrap\" class=\"ft460\">Therefore&nbsp;<\/p>\n<p style=\"position:absolute;top:1022px;left:271px;white-space:nowrap\" class=\"ft460\">(a&nbsp;+ b) sin&nbsp;(&theta;n+d&theta;) = n&nbsp;&lambda;&nbsp;+&nbsp;&lambda;&nbsp;\/N&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:1022px;left:541px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1022px;left:595px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1022px;left:649px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1022px;left:703px;white-space:nowrap\" class=\"ft460\">&nbsp;(iii)&nbsp;<\/p>\n<p style=\"position:absolute;top:1044px;left:271px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1066px;left:163px;white-space:nowrap\" class=\"ft460\">Equating&nbsp;the&nbsp;right hand sides&nbsp;of (ii)&nbsp;and (iii)&nbsp;<\/p>\n<p style=\"position:absolute;top:1088px;left:163px;white-space:nowrap\" class=\"ft460\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1110px;left:163px;white-space:nowrap\" class=\"ft460\">n (&lambda;&nbsp;+d&nbsp;&lambda;)&nbsp;= n&nbsp;&lambda;&nbsp;+&nbsp;&lambda;&nbsp;\/N&nbsp;<\/p>\n<\/div>\n<div id=\"page47-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559047.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft470\">23&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:163px;white-space:nowrap\" class=\"ft470\">&lambda;\/d&nbsp;&lambda;&nbsp;=nN&nbsp;<\/p>\n<p style=\"position:absolute;top:68px;left:163px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:90px;left:163px;white-space:nowrap\" class=\"ft470\">The&nbsp;quantity&nbsp;&lambda;&nbsp;\/d&lambda;&nbsp;=&nbsp;nN&nbsp;measures&nbsp;the&nbsp;resolving&nbsp;power&nbsp;of a&nbsp;grating.&nbsp;<\/p>\n<p style=\"position:absolute;top:112px;left:163px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:134px;left:163px;white-space:nowrap\" class=\"ft470\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:157px;left:187px;white-space:nowrap\" class=\"ft470\">S.NO&nbsp;<\/p>\n<p style=\"position:absolute;top:157px;left:307px;white-space:nowrap\" class=\"ft470\">RGPV QUESTION&nbsp;<\/p>\n<p style=\"position:absolute;top:157px;left:550px;white-space:nowrap\" class=\"ft470\">YEAR&nbsp;<\/p>\n<p style=\"position:absolute;top:157px;left:702px;white-space:nowrap\" class=\"ft470\">MARKS&nbsp;<\/p>\n<p style=\"position:absolute;top:179px;left:172px;white-space:nowrap\" class=\"ft470\">Q.1&nbsp;<\/p>\n<p style=\"position:absolute;top:179px;left:255px;white-space:nowrap\" class=\"ft470\">Obtain the&nbsp;expression for&nbsp;<\/p>\n<p style=\"position:absolute;top:201px;left:255px;white-space:nowrap\" class=\"ft470\">resolving&nbsp;&nbsp;power&nbsp;of&nbsp;plane&nbsp;<\/p>\n<p style=\"position:absolute;top:223px;left:255px;white-space:nowrap\" class=\"ft470\">transmission&nbsp;grating.&nbsp;<\/p>\n<p style=\"position:absolute;top:179px;left:535px;white-space:nowrap\" class=\"ft470\">Dec&nbsp;2012&nbsp;<\/p>\n<p style=\"position:absolute;top:179px;left:720px;white-space:nowrap\" class=\"ft470\">10&nbsp;<\/p>\n<p style=\"position:absolute;top:246px;left:163px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:268px;left:163px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:291px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:313px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:335px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:357px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:357px;left:497px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:379px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:401px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:423px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:445px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:467px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:489px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:510px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:533px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:554px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:576px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:598px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:620px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:642px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:664px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:686px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:708px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:730px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:752px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:774px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:796px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:818px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:840px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:862px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:884px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:906px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:928px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:950px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:972px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:994px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1016px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1038px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1060px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1082px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1104px;left:108px;white-space:nowrap\" class=\"ft470\">&nbsp;<\/p>\n<\/div>\n<div id=\"page48-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559048.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft480\">24&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft484\">&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:67px;left:108px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:89px;left:108px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:111px;left:108px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:140px;left:150px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:175px;left:404px;white-space:nowrap\" class=\"ft481\"><b>UNIT-2\/&nbsp;LECTURE 10&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:218px;left:150px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:261px;left:150px;white-space:nowrap\" class=\"ft481\"><b>Prism Resolving&nbsp;Power&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:305px;left:150px;white-space:nowrap\" class=\"ft480\">The&nbsp;term resolving&nbsp;power is&nbsp;applied&nbsp;to&nbsp;spectrographic&nbsp;devices&nbsp;using&nbsp;a prism or a grating.&nbsp;<\/p>\n<p style=\"position:absolute;top:327px;left:150px;white-space:nowrap\" class=\"ft480\">Resolving&nbsp;power signifies&nbsp;the&nbsp;ability&nbsp;of&nbsp;the&nbsp;instrument&nbsp;to&nbsp;form separate&nbsp;spectral images&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:349px;left:150px;white-space:nowrap\" class=\"ft480\">two&nbsp;neighbouring&nbsp;wavelengths,<\/p>\n<p style=\"position:absolute;top:348px;left:379px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b>&lambda;<b>&nbsp;<\/b>and&nbsp;&lambda;&nbsp;+&nbsp;d&lambda;&nbsp;in the&nbsp;wavelength region&nbsp;&lambda;.&nbsp;<\/p>\n<p style=\"position:absolute;top:667px;left:803px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:684px;left:150px;white-space:nowrap\" class=\"ft480\">In&nbsp;fig.&nbsp;S&nbsp;is&nbsp;a source&nbsp;of&nbsp;light,&nbsp;<\/p>\n<p style=\"position:absolute;top:684px;left:347px;white-space:nowrap\" class=\"ft481\"><b>L<\/b><\/p>\n<p style=\"position:absolute;top:692px;left:355px;white-space:nowrap\" class=\"ft482\"><b>1<\/b><\/p>\n<p style=\"position:absolute;top:684px;left:361px;white-space:nowrap\" class=\"ft480\">&nbsp;is&nbsp;a collimating&nbsp;lens&nbsp;and&nbsp;L<\/p>\n<p style=\"position:absolute;top:692px;left:550px;white-space:nowrap\" class=\"ft483\">2<\/p>\n<p style=\"position:absolute;top:684px;left:556px;white-space:nowrap\" class=\"ft480\">&nbsp;is&nbsp;the&nbsp;telescope&nbsp;objective.&nbsp;As&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:706px;left:150px;white-space:nowrap\" class=\"ft480\">two&nbsp;wavelengths&nbsp;&lambda;&nbsp;and&nbsp;&lambda;&nbsp;+&nbsp;d&lambda;&nbsp;are&nbsp;very&nbsp;close,&nbsp;if&nbsp;the&nbsp;prism is&nbsp;set&nbsp;in&nbsp;the&nbsp;minimum deviation&nbsp;<\/p>\n<p style=\"position:absolute;top:728px;left:150px;white-space:nowrap\" class=\"ft480\">position it would hold good for&nbsp;both&nbsp;the&nbsp;wavelengths.&nbsp;The&nbsp;final&nbsp;image<\/p>\n<p style=\"position:absolute;top:728px;left:657px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b>I<\/p>\n<p style=\"position:absolute;top:736px;left:666px;white-space:nowrap\" class=\"ft483\">1<\/p>\n<p style=\"position:absolute;top:728px;left:672px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b>corresponds&nbsp;to&nbsp;<\/p>\n<p style=\"position:absolute;top:750px;left:150px;white-space:nowrap\" class=\"ft480\">the&nbsp;principal&nbsp;maximum for wavelength<\/p>\n<p style=\"position:absolute;top:750px;left:432px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b>&lambda;<b>&nbsp;<\/b>and&nbsp;image<b>&nbsp;I<\/b><\/p>\n<p style=\"position:absolute;top:758px;left:533px;white-space:nowrap\" class=\"ft482\"><b>2<\/b><\/p>\n<p style=\"position:absolute;top:750px;left:539px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b>corresponds&nbsp;to&nbsp;the&nbsp;principal&nbsp;<\/p>\n<p style=\"position:absolute;top:772px;left:150px;white-space:nowrap\" class=\"ft480\">maximum for wavelength,&nbsp;&lambda;&nbsp;+&nbsp;d&lambda;.&nbsp;I<\/p>\n<p style=\"position:absolute;top:780px;left:401px;white-space:nowrap\" class=\"ft483\">1<\/p>\n<p style=\"position:absolute;top:772px;left:407px;white-space:nowrap\" class=\"ft480\">&nbsp;and<\/p>\n<p style=\"position:absolute;top:771px;left:439px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b>I<\/p>\n<p style=\"position:absolute;top:780px;left:447px;white-space:nowrap\" class=\"ft483\">2<\/p>\n<p style=\"position:absolute;top:771px;left:453px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b>are&nbsp;formed at the&nbsp;focal&nbsp;plane&nbsp;of the&nbsp;telescope&nbsp;<\/p>\n<p style=\"position:absolute;top:794px;left:150px;white-space:nowrap\" class=\"ft480\">objective&nbsp;L<\/p>\n<p style=\"position:absolute;top:802px;left:228px;white-space:nowrap\" class=\"ft483\">2<\/p>\n<p style=\"position:absolute;top:794px;left:234px;white-space:nowrap\" class=\"ft480\">.&nbsp;The&nbsp;face&nbsp;of the&nbsp;prism&nbsp;limits&nbsp;the&nbsp;incident beam&nbsp;to&nbsp;a&nbsp;rectangular&nbsp;section of&nbsp;<\/p>\n<p style=\"position:absolute;top:816px;left:150px;white-space:nowrap\" class=\"ft480\">width a.&nbsp;Hence, the&nbsp;Rayleigh criterion can be&nbsp;applied in the&nbsp;case&nbsp;of a&nbsp;rectangular&nbsp;aperture.&nbsp;<\/p>\n<p style=\"position:absolute;top:838px;left:150px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:860px;left:150px;white-space:nowrap\" class=\"ft480\">In the&nbsp;case&nbsp;of diffraction at a&nbsp;rectangular&nbsp;aperture, the&nbsp;position of<\/p>\n<p style=\"position:absolute;top:859px;left:629px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b>I<\/p>\n<p style=\"position:absolute;top:868px;left:638px;white-space:nowrap\" class=\"ft483\">2<\/p>\n<p style=\"position:absolute;top:859px;left:644px;white-space:nowrap\" class=\"ft481\"><b>&nbsp;<\/b>will&nbsp;correspond&nbsp;to&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:882px;left:150px;white-space:nowrap\" class=\"ft480\">first&nbsp;minimum of&nbsp;the&nbsp;image&nbsp;I<\/p>\n<p style=\"position:absolute;top:890px;left:357px;white-space:nowrap\" class=\"ft483\">1<\/p>\n<p style=\"position:absolute;top:882px;left:363px;white-space:nowrap\" class=\"ft480\">&nbsp;for&nbsp;wavelength&nbsp;&lambda;<\/p>\n<p style=\"position:absolute;top:890px;left:489px;white-space:nowrap\" class=\"ft483\">1<\/p>\n<p style=\"position:absolute;top:882px;left:495px;white-space:nowrap\" class=\"ft480\">&nbsp;provided&nbsp;<\/p>\n<p style=\"position:absolute;top:904px;left:150px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:925px;left:150px;white-space:nowrap\" class=\"ft481\"><b>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;<\/b>a.d&delta;&nbsp;=&nbsp;&lambda;&nbsp;<\/p>\n<p style=\"position:absolute;top:948px;left:150px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:969px;left:150px;white-space:nowrap\" class=\"ft480\">or,&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;d&delta;&nbsp;=&nbsp;&lambda;\/a&nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;(i)&nbsp;<\/p>\n<p style=\"position:absolute;top:991px;left:150px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1013px;left:150px;white-space:nowrap\" class=\"ft480\">Here,&nbsp;&delta;&nbsp;is&nbsp;the&nbsp;angle&nbsp;of&nbsp;minimum deviation&nbsp;for wavelength&nbsp;&lambda;.&nbsp;<\/p>\n<p style=\"position:absolute;top:1035px;left:150px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1057px;left:150px;white-space:nowrap\" class=\"ft480\">From&nbsp;the&nbsp;figure,&nbsp;<\/p>\n<p style=\"position:absolute;top:1079px;left:150px;white-space:nowrap\" class=\"ft480\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1101px;left:150px;white-space:nowrap\" class=\"ft481\"><b>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;<\/b>&alpha;+&nbsp;A&nbsp;+&nbsp;&alpha;&nbsp;+&nbsp;&delta;&nbsp;=&nbsp;&pi;&nbsp;<\/p>\n<\/div>\n<div id=\"page49-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559049.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft490\">25&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:49px;left:150px;white-space:nowrap\" class=\"ft491\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:366px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;<\/p>\n<p style=\"position:absolute;top:366px;left:554px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:383px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:426px;left:150px;white-space:nowrap\" class=\"ft490\">In the&nbsp;case&nbsp;of a&nbsp;prism&nbsp;<\/p>\n<p style=\"position:absolute;top:469px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:512px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:555px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:555px;left:255px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:598px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:620px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:642px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:664px;left:150px;white-space:nowrap\" class=\"ft490\">Here and&nbsp;&delta;&nbsp;are&nbsp;dependent on wavelength of light&nbsp;&lambda;.&nbsp;<\/p>\n<p style=\"position:absolute;top:686px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:708px;left:150px;white-space:nowrap\" class=\"ft490\">Differentiating&nbsp;equation (iv)<\/p>\n<p style=\"position:absolute;top:708px;left:352px;white-space:nowrap\" class=\"ft491\"><b>&nbsp;<\/b>with respect to&nbsp;<\/p>\n<p style=\"position:absolute;top:730px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:805px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;<\/p>\n<p style=\"position:absolute;top:805px;left:573px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:822px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:844px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:866px;left:150px;white-space:nowrap\" class=\"ft490\">Substituting&nbsp;the&nbsp;values&nbsp;from&nbsp;equations&nbsp;(ii)&nbsp;and&nbsp;(iii),&nbsp;<\/p>\n<p style=\"position:absolute;top:1003px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:1003px;left:553px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1041px;left:150px;white-space:nowrap\" class=\"ft490\">Substituting&nbsp;the&nbsp;value&nbsp;of&nbsp;d&delta;&nbsp;from&nbsp;equation (i),&nbsp;<\/p>\n<p style=\"position:absolute;top:1084px;left:150px;white-space:nowrap\" class=\"ft490\">&nbsp;<\/p>\n<\/div>\n<div id=\"page50-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559050.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft500\">26&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:73px;left:150px;white-space:nowrap\" class=\"ft500\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:73px;left:552px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:90px;left:150px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:112px;left:150px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:134px;left:150px;white-space:nowrap\" class=\"ft500\">The&nbsp;expression&nbsp;&lambda;\/d&lambda;&nbsp;measures&nbsp;the&nbsp;resolving&nbsp;power&nbsp;of the&nbsp;prism.&nbsp;It is&nbsp;defined as&nbsp;the&nbsp;ratio&nbsp;<\/p>\n<p style=\"position:absolute;top:156px;left:150px;white-space:nowrap\" class=\"ft500\">of the&nbsp;wavelength of a&nbsp;spectral&nbsp;line&nbsp;to&nbsp;the&nbsp;difference&nbsp;in wavelength between the&nbsp;line&nbsp;and a&nbsp;<\/p>\n<p style=\"position:absolute;top:178px;left:150px;white-space:nowrap\" class=\"ft500\">neighbouring&nbsp;line&nbsp;such that the&nbsp;two&nbsp;lines&nbsp;appear&nbsp;just resolved, according&nbsp;to&nbsp;Rayleigh&rsquo;s&nbsp;<\/p>\n<p style=\"position:absolute;top:200px;left:150px;white-space:nowrap\" class=\"ft500\">criterion.&nbsp;<\/p>\n<p style=\"position:absolute;top:222px;left:150px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:290px;left:150px;white-space:nowrap\" class=\"ft500\">&nbsp; &nbsp; &nbsp; &nbsp;<\/p>\n<p style=\"position:absolute;top:290px;left:457px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:328px;left:150px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:350px;left:150px;white-space:nowrap\" class=\"ft500\">Thus,&nbsp;the&nbsp;resolving&nbsp;power of&nbsp;a prism is<\/p>\n<p style=\"position:absolute;top:350px;left:431px;white-space:nowrap\" class=\"ft501\"><b>&nbsp;<\/b>(i)&nbsp;directly&nbsp;proportional&nbsp;to&nbsp;the&nbsp;length of the&nbsp;base&nbsp;<\/p>\n<p style=\"position:absolute;top:372px;left:150px;white-space:nowrap\" class=\"ft500\">and&nbsp;(ii)&nbsp;rate&nbsp;of change&nbsp;of&nbsp;refractive&nbsp;index&nbsp;with respect to&nbsp;wavelength for&nbsp;that particular&nbsp;<\/p>\n<p style=\"position:absolute;top:394px;left:150px;white-space:nowrap\" class=\"ft500\">material.&nbsp;<\/p>\n<p style=\"position:absolute;top:437px;left:480px;white-space:nowrap\" class=\"ft501\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:460px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:482px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:504px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:526px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:548px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:570px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:592px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:614px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:636px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:658px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:680px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:702px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:724px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:746px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:768px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:790px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:812px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:834px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:856px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:878px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:900px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:922px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:944px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:966px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:987px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1009px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1031px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1053px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1075px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1097px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1119px;left:108px;white-space:nowrap\" class=\"ft500\">&nbsp;<\/p>\n<\/div>\n<div id=\"page51-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559051.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft510\">27&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft512\">&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:67px;left:108px;white-space:nowrap\" class=\"ft510\">&nbsp;<\/p>\n<p style=\"position:absolute;top:89px;left:108px;white-space:nowrap\" class=\"ft510\">&nbsp;<\/p>\n<p style=\"position:absolute;top:112px;left:386px;white-space:nowrap\" class=\"ft511\"><b>UNIT&nbsp;2\/LECTURE 11&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:173px;left:108px;white-space:nowrap\" class=\"ft511\"><b>Concept&nbsp;of polarized&nbsp;light:&nbsp;[RGPV\/Dec2011\/(4)]&nbsp;&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:195px;left:108px;white-space:nowrap\" class=\"ft511\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:217px;left:108px;white-space:nowrap\" class=\"ft511\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:239px;left:108px;white-space:nowrap\" class=\"ft511\"><b>Unpolarized light:<\/b>&nbsp;The&nbsp;ordinary&nbsp;light&nbsp;is&nbsp;also&nbsp;called&nbsp;unpolarized&nbsp;light,&nbsp;consist&nbsp;of&nbsp;very&nbsp;large&nbsp;<\/p>\n<p style=\"position:absolute;top:261px;left:108px;white-space:nowrap\" class=\"ft510\">number&nbsp;of vibrations&nbsp;in&nbsp;all&nbsp;planes&nbsp;with equal&nbsp;probability&nbsp;at right angles&nbsp;to&nbsp;the&nbsp;direction of&nbsp;<\/p>\n<p style=\"position:absolute;top:283px;left:108px;white-space:nowrap\" class=\"ft510\">propagation.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:305px;left:108px;white-space:nowrap\" class=\"ft510\">&nbsp;<\/p>\n<p style=\"position:absolute;top:646px;left:108px;white-space:nowrap\" class=\"ft510\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:646px;left:466px;white-space:nowrap\" class=\"ft510\">&nbsp;<\/p>\n<p style=\"position:absolute;top:663px;left:108px;white-space:nowrap\" class=\"ft511\"><b>Linearly&nbsp;(Plane),&nbsp;circularly&nbsp;and&nbsp;elliptically&nbsp;polarized&nbsp;light&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:686px;left:108px;white-space:nowrap\" class=\"ft510\">The&nbsp;light which has&nbsp;acquired the&nbsp;property&nbsp;of one&nbsp;sidedness&nbsp;is&nbsp;called polarized light.&nbsp;When the&nbsp;<\/p>\n<p style=\"position:absolute;top:708px;left:108px;white-space:nowrap\" class=\"ft510\">vibrations&nbsp;are&nbsp;confined along&nbsp;a&nbsp;single&nbsp;direction at right angle&nbsp;to&nbsp;the&nbsp;direction of&nbsp;propagation of&nbsp;<\/p>\n<p style=\"position:absolute;top:730px;left:108px;white-space:nowrap\" class=\"ft510\">light, then the&nbsp;light&nbsp;is&nbsp;called&nbsp;plane&nbsp;polarized&nbsp;light.&nbsp;<\/p>\n<p style=\"position:absolute;top:751px;left:108px;white-space:nowrap\" class=\"ft510\">&nbsp;<\/p>\n<p style=\"position:absolute;top:915px;left:574px;white-space:nowrap\" class=\"ft510\">&nbsp;<\/p>\n<p style=\"position:absolute;top:932px;left:108px;white-space:nowrap\" class=\"ft510\">&nbsp;<\/p>\n<p style=\"position:absolute;top:954px;left:108px;white-space:nowrap\" class=\"ft510\">&nbsp;<\/p>\n<p style=\"position:absolute;top:976px;left:108px;white-space:nowrap\" class=\"ft510\">Light is&nbsp;an electromagnetic&nbsp;that vibrates&nbsp;at very&nbsp;high speed back and forth as&nbsp;it moves.&nbsp;<\/p>\n<p style=\"position:absolute;top:998px;left:108px;white-space:nowrap\" class=\"ft510\">Individual&nbsp;light waves&nbsp;have&nbsp;their&nbsp;own wavelength as&nbsp;well&nbsp;as&nbsp;angle&nbsp;of vibration, which can range&nbsp;<\/p>\n<p style=\"position:absolute;top:1020px;left:108px;white-space:nowrap\" class=\"ft510\">through&nbsp;a&nbsp;full&nbsp;of&nbsp;360&deg;.&nbsp;The&nbsp;angle&nbsp;of vibration of a&nbsp;light wave&nbsp;is&nbsp;defined by&nbsp;its&nbsp;electric&nbsp;and&nbsp;<\/p>\n<p style=\"position:absolute;top:1042px;left:108px;white-space:nowrap\" class=\"ft510\">magnetic&nbsp;components&nbsp;(vectors)&nbsp;that&nbsp;are&nbsp;perpendicular&nbsp;to&nbsp;each other&nbsp;and to&nbsp;the&nbsp;direction of the&nbsp;<\/p>\n<p style=\"position:absolute;top:1064px;left:108px;white-space:nowrap\" class=\"ft510\">wave&nbsp;propagation.&nbsp;Ordinary&nbsp;visible&nbsp;light is&nbsp;unpolarized, i.e.&nbsp;it is&nbsp;composed of many&nbsp;different&nbsp;<\/p>\n<p style=\"position:absolute;top:1086px;left:108px;white-space:nowrap\" class=\"ft510\">waves&nbsp;vibrating&nbsp;in&nbsp;all directions.&nbsp;A plane&nbsp;electromagnetic&nbsp;wave&nbsp;is&nbsp;said&nbsp;to&nbsp;be&nbsp;<\/p>\n<p style=\"position:absolute;top:1086px;left:659px;white-space:nowrap\" class=\"ft511\"><b>linearly&nbsp;polarized<\/b>.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:1108px;left:108px;white-space:nowrap\" class=\"ft511\"><b>Circularly&nbsp;polarized<\/b>&nbsp;light consists&nbsp;of&nbsp;two&nbsp;perpendicular&nbsp;electromagnetic&nbsp;plane&nbsp;waves&nbsp;of equal&nbsp;<\/p>\n<\/div>\n<div id=\"page52-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559052.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft520\">28&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft522\">&nbsp;<br \/>amplitude&nbsp;and 90&deg;&nbsp;difference&nbsp;in phase.&nbsp;<\/p>\n<p style=\"position:absolute;top:389px;left:108px;white-space:nowrap\" class=\"ft521\"><b>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:389px;left:488px;white-space:nowrap\" class=\"ft521\"><b>Circularly&nbsp;polarized&nbsp;light&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:423px;left:108px;white-space:nowrap\" class=\"ft520\">Elliptically&nbsp;polarized light consists&nbsp;of&nbsp;two&nbsp;perpendicular&nbsp;waves&nbsp;of unequal&nbsp;amplitude&nbsp;which differ&nbsp;<\/p>\n<p style=\"position:absolute;top:444px;left:108px;white-space:nowrap\" class=\"ft520\">in phase&nbsp;by&nbsp;90&deg;&nbsp;<\/p>\n<p style=\"position:absolute;top:466px;left:108px;white-space:nowrap\" class=\"ft520\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:466px;left:153px;white-space:nowrap\" class=\"ft521\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:794px;left:108px;white-space:nowrap\" class=\"ft521\"><b>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:794px;left:524px;white-space:nowrap\" class=\"ft521\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:811px;left:108px;white-space:nowrap\" class=\"ft521\"><b>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;Elliptically&nbsp;Polarized&nbsp;light&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:833px;left:108px;white-space:nowrap\" class=\"ft520\">&nbsp;<\/p>\n<p style=\"position:absolute;top:855px;left:108px;white-space:nowrap\" class=\"ft521\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:877px;left:108px;white-space:nowrap\" class=\"ft521\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:899px;left:108px;white-space:nowrap\" class=\"ft521\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:921px;left:108px;white-space:nowrap\" class=\"ft521\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:943px;left:108px;white-space:nowrap\" class=\"ft521\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:965px;left:108px;white-space:nowrap\" class=\"ft521\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:987px;left:108px;white-space:nowrap\" class=\"ft521\"><b>Brewsters&nbsp;Law&nbsp;:&nbsp;[RGPV\/JUNE2013 (4)]&nbsp;&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:1009px;left:108px;white-space:nowrap\" class=\"ft520\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1031px;left:108px;white-space:nowrap\" class=\"ft520\">When&nbsp;ordinary&nbsp;light&nbsp;is&nbsp;reflected&nbsp;from the&nbsp;surface&nbsp;of&nbsp;transparent&nbsp;medium like&nbsp;glass&nbsp;or water it&nbsp;<\/p>\n<p style=\"position:absolute;top:1053px;left:108px;white-space:nowrap\" class=\"ft520\">becomes&nbsp;partly&nbsp;polarized.&nbsp;The&nbsp;degree&nbsp;of&nbsp;polarization&nbsp;changes&nbsp;with the&nbsp;angle&nbsp;of incidence.&nbsp;At a&nbsp;<\/p>\n<p style=\"position:absolute;top:1075px;left:108px;white-space:nowrap\" class=\"ft520\">particular&nbsp;angle&nbsp;of incidence&nbsp;the&nbsp;reflected light has&nbsp;the&nbsp;greatest percentage&nbsp;of polarized light&nbsp;<\/p>\n<p style=\"position:absolute;top:1097px;left:108px;white-space:nowrap\" class=\"ft520\">.The&nbsp;angle&nbsp;at&nbsp;which&nbsp;the&nbsp;reflected&nbsp;light&nbsp;is&nbsp;completely&nbsp;plane&nbsp;polarized,&nbsp;is&nbsp;known&nbsp;as&nbsp;angle&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:1119px;left:108px;white-space:nowrap\" class=\"ft520\">polarization.&nbsp;<\/p>\n<\/div>\n<div id=\"page53-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559053.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft530\">29&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft533\">&nbsp;<br \/>&nbsp;<\/p>\n<p style=\"position:absolute;top:68px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:90px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:112px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:134px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:156px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:178px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:200px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:222px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:244px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:266px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:288px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:310px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:332px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:354px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:376px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:398px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:420px;left:108px;white-space:nowrap\" class=\"ft530\">According&nbsp;to&nbsp;Brewster&rsquo;s&nbsp;law&nbsp;&ldquo;tangent&nbsp;of&nbsp;angle&nbsp;of&nbsp;polarization&nbsp;&Theta;<\/p>\n<p style=\"position:absolute;top:428px;left:567px;white-space:nowrap\" class=\"ft531\">i&nbsp;<\/p>\n<p style=\"position:absolute;top:420px;left:572px;white-space:nowrap\" class=\"ft530\">is&nbsp;numerically&nbsp;equal to&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:442px;left:108px;white-space:nowrap\" class=\"ft530\">refractive&nbsp;index&nbsp;&micro; of the&nbsp;medium&rdquo;.&nbsp;<\/p>\n<p style=\"position:absolute;top:464px;left:426px;white-space:nowrap\" class=\"ft530\">&micro;=&nbsp;tan&nbsp;&Theta;<\/p>\n<p style=\"position:absolute;top:472px;left:489px;white-space:nowrap\" class=\"ft531\">i&nbsp;<\/p>\n<p style=\"position:absolute;top:485px;left:108px;white-space:nowrap\" class=\"ft534\"><b>&nbsp;<br \/>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;<\/b>From&nbsp;Brewster&rsquo;s&nbsp;law&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:540px;left:402px;white-space:nowrap\" class=\"ft530\">&micro;=&nbsp;tan&nbsp;&Theta;<\/p>\n<p style=\"position:absolute;top:549px;left:465px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:540px;left:468px;white-space:nowrap\" class=\"ft530\">&#8212;&#8212;(i)&nbsp;<\/p>\n<p style=\"position:absolute;top:562px;left:108px;white-space:nowrap\" class=\"ft530\">From&nbsp;Snell&rsquo;s&nbsp;law&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:584px;left:254px;white-space:nowrap\" class=\"ft530\">&micro;=sin&nbsp;&Theta;<\/p>\n<p style=\"position:absolute;top:593px;left:309px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:584px;left:312px;white-space:nowrap\" class=\"ft530\">\/ sin&nbsp;r&#8212;&#8212;&#8212;(ii)&nbsp; &nbsp;&nbsp; (where&nbsp;r is&nbsp;angle&nbsp;of&nbsp;refraction)&nbsp;<\/p>\n<p style=\"position:absolute;top:606px;left:459px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:628px;left:390px;white-space:nowrap\" class=\"ft530\">tan&nbsp;&Theta;<\/p>\n<p style=\"position:absolute;top:637px;left:430px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:628px;left:433px;white-space:nowrap\" class=\"ft530\">=&nbsp;sin&nbsp;&Theta;<\/p>\n<p style=\"position:absolute;top:637px;left:483px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:628px;left:485px;white-space:nowrap\" class=\"ft530\">\/ sin&nbsp;r&nbsp;<\/p>\n<p style=\"position:absolute;top:650px;left:362px;white-space:nowrap\" class=\"ft530\">sinr=&nbsp;cos &Theta;<\/p>\n<p style=\"position:absolute;top:659px;left:442px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:650px;left:445px;white-space:nowrap\" class=\"ft530\">&#8212;&#8212;&#8212;&#8212;&#8212;-(iii)&nbsp;<\/p>\n<p style=\"position:absolute;top:672px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:694px;left:108px;white-space:nowrap\" class=\"ft530\">From fig.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:716px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;r+&nbsp;&Theta;<\/p>\n<p style=\"position:absolute;top:725px;left:253px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:716px;left:256px;white-space:nowrap\" class=\"ft530\">+&Theta;=&nbsp;180&nbsp;&#8212;&#8212;-(iv)&nbsp; (where&nbsp;&Theta;&nbsp;is angle&nbsp;between&nbsp;reflected&nbsp;ray&nbsp;and refracted&nbsp;<\/p>\n<p style=\"position:absolute;top:738px;left:108px;white-space:nowrap\" class=\"ft530\">ray)&nbsp;<\/p>\n<p style=\"position:absolute;top:760px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;From equation&nbsp;(iii)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:800px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;sin&nbsp;r=sin(90-&Theta;<\/p>\n<p style=\"position:absolute;top:809px;left:307px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:800px;left:310px;white-space:nowrap\" class=\"ft530\">)&nbsp;<\/p>\n<p style=\"position:absolute;top:840px;left:108px;white-space:nowrap\" class=\"ft530\">sin&nbsp;r=sin(90-&Theta;<\/p>\n<p style=\"position:absolute;top:849px;left:210px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:840px;left:212px;white-space:nowrap\" class=\"ft530\">)&nbsp;<\/p>\n<p style=\"position:absolute;top:880px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;r=&nbsp;90-&Theta;<\/p>\n<p style=\"position:absolute;top:889px;left:248px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:880px;left:251px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:920px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;r+&nbsp;&Theta;<\/p>\n<p style=\"position:absolute;top:928px;left:229px;white-space:nowrap\" class=\"ft531\">i<\/p>\n<p style=\"position:absolute;top:920px;left:232px;white-space:nowrap\" class=\"ft530\">=90&#8212;&#8212;&#8212;-(v)&nbsp;<\/p>\n<p style=\"position:absolute;top:960px;left:108px;white-space:nowrap\" class=\"ft530\">From&nbsp;equation (iv)&nbsp;and equation (v)&nbsp;<\/p>\n<p style=\"position:absolute;top:1000px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&Theta;=90&deg;&nbsp;<\/p>\n<p style=\"position:absolute;top:1040px;left:108px;white-space:nowrap\" class=\"ft530\">Therefore&nbsp;we&nbsp;can say&nbsp;that reflected ray&nbsp;and refracted ray&nbsp;are&nbsp;at right angle&nbsp;to&nbsp;each other.&nbsp;<\/p>\n<p style=\"position:absolute;top:1080px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<p style=\"position:absolute;top:1120px;left:108px;white-space:nowrap\" class=\"ft530\">&nbsp;<\/p>\n<\/div>\n<div id=\"page54-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559054.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft540\">30&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft540\">&nbsp;<\/p>\n<p style=\"position:absolute;top:64px;left:108px;white-space:nowrap\" class=\"ft540\">&nbsp;<\/p>\n<p style=\"position:absolute;top:86px;left:108px;white-space:nowrap\" class=\"ft541\"><b>Plane&nbsp;of vibration&nbsp;and&nbsp;plane&nbsp;of Polarization&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:108px;left:108px;white-space:nowrap\" class=\"ft540\">The&nbsp;plane&nbsp;which contains&nbsp;the&nbsp;direction of&nbsp;vibration of electric&nbsp;vector&nbsp;in plane&nbsp;polarized light is&nbsp;<\/p>\n<p style=\"position:absolute;top:130px;left:108px;white-space:nowrap\" class=\"ft540\">called plane&nbsp;of vibration.&nbsp;<\/p>\n<p style=\"position:absolute;top:170px;left:108px;white-space:nowrap\" class=\"ft540\">The&nbsp;plane&nbsp;perpendicular&nbsp;to&nbsp;the&nbsp;plane&nbsp;of vibration and passing&nbsp;through the&nbsp;direction of light is&nbsp;<\/p>\n<p style=\"position:absolute;top:192px;left:108px;white-space:nowrap\" class=\"ft540\">called&nbsp;plane&nbsp;of&nbsp;polarization.&nbsp;<\/p>\n<p style=\"position:absolute;top:232px;left:108px;white-space:nowrap\" class=\"ft540\">&nbsp;<\/p>\n<p style=\"position:absolute;top:254px;left:108px;white-space:nowrap\" class=\"ft541\"><b>&nbsp; &nbsp;&nbsp;Double&nbsp;refraction and doubly&nbsp;refracting&nbsp;crystal&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:276px;left:108px;white-space:nowrap\" class=\"ft540\">When a&nbsp;beam&nbsp;of light is&nbsp;allowed to&nbsp;pass&nbsp;through&nbsp;certain&nbsp;crystal,&nbsp;it&nbsp;splits&nbsp;in&nbsp;two&nbsp;refracting&nbsp;rays&nbsp;<\/p>\n<p style=\"position:absolute;top:298px;left:108px;white-space:nowrap\" class=\"ft540\">instead of one, such crystals&nbsp;are&nbsp;called doubly&nbsp;refracting&nbsp;crystals&nbsp;and this&nbsp;phenomenon is&nbsp;known&nbsp;<\/p>\n<p style=\"position:absolute;top:320px;left:108px;white-space:nowrap\" class=\"ft540\">as&nbsp;double&nbsp;refraction.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:342px;left:108px;white-space:nowrap\" class=\"ft540\">&nbsp;<\/p>\n<p style=\"position:absolute;top:364px;left:108px;white-space:nowrap\" class=\"ft541\"><b>&nbsp; &nbsp; &nbsp;&nbsp;<\/b>When unpolarized light enters&nbsp;in&nbsp;doubly&nbsp;refracting&nbsp;crystals&nbsp;it splits&nbsp;in two&nbsp;refracting&nbsp;rays:&nbsp;<\/p>\n<p style=\"position:absolute;top:404px;left:135px;white-space:nowrap\" class=\"ft540\">1.&nbsp;&nbsp;&nbsp;Out of&nbsp;these&nbsp;two&nbsp;rays&nbsp;one&nbsp;ray&nbsp;obey&nbsp;the&nbsp;law obey&nbsp;the&nbsp;law of refraction (<i>&micro;&nbsp;<\/i>=&nbsp;sin&nbsp;&#119904;&#119904;&nbsp;\/&nbsp;sin&nbsp;&#119903;&#119903;),&nbsp;<\/p>\n<p style=\"position:absolute;top:429px;left:162px;white-space:nowrap\" class=\"ft544\">is&nbsp;called ordinary&nbsp;ray, on the&nbsp;other&nbsp;hand other&nbsp;refracted ray&nbsp;does&nbsp;not&nbsp;obey&nbsp;law of&nbsp;<br \/>refraction&nbsp;is&nbsp;called&nbsp;extraordinary&nbsp;ray.&nbsp;<\/p>\n<p style=\"position:absolute;top:479px;left:135px;white-space:nowrap\" class=\"ft540\">2.&nbsp;&nbsp;Inside&nbsp;the&nbsp;crystal&nbsp;the&nbsp;speed of&nbsp;both&nbsp;ordinary&nbsp;and&nbsp;extraordinary&nbsp;ray&nbsp;is&nbsp;same&nbsp;along&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:505px;left:162px;white-space:nowrap\" class=\"ft544\">optic&nbsp;axes&nbsp;and hence&nbsp;the&nbsp;refractive&nbsp;index&nbsp;of the&nbsp;crystal&nbsp;is&nbsp;also&nbsp;same&nbsp;along&nbsp;the&nbsp;optic&nbsp;axes&nbsp;<br \/>for&nbsp;both the&nbsp;rays&nbsp;(i.e.&nbsp;along&nbsp;optic&nbsp;axes&nbsp;v<\/p>\n<p style=\"position:absolute;top:538px;left:448px;white-space:nowrap\" class=\"ft543\">o<\/p>\n<p style=\"position:absolute;top:530px;left:454px;white-space:nowrap\" class=\"ft540\">=v<\/p>\n<p style=\"position:absolute;top:538px;left:471px;white-space:nowrap\" class=\"ft543\">e<\/p>\n<p style=\"position:absolute;top:530px;left:477px;white-space:nowrap\" class=\"ft540\">&nbsp;and &micro;<\/p>\n<p style=\"position:absolute;top:538px;left:523px;white-space:nowrap\" class=\"ft543\">o<\/p>\n<p style=\"position:absolute;top:530px;left:529px;white-space:nowrap\" class=\"ft540\">=&micro;<\/p>\n<p style=\"position:absolute;top:538px;left:548px;white-space:nowrap\" class=\"ft543\">e<\/p>\n<p style=\"position:absolute;top:530px;left:554px;white-space:nowrap\" class=\"ft540\">).&nbsp;Obviously&nbsp;if the&nbsp;light ray&nbsp;enter&nbsp;in&nbsp;<\/p>\n<p style=\"position:absolute;top:555px;left:162px;white-space:nowrap\" class=\"ft540\">the&nbsp;crystal along&nbsp;optic&nbsp;axes&nbsp;there&nbsp;will&nbsp;no&nbsp;double&nbsp;refraction.&nbsp;<\/p>\n<p style=\"position:absolute;top:598px;left:108px;white-space:nowrap\" class=\"ft541\"><b>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;Types&nbsp;of&nbsp;doubly&nbsp;refracting&nbsp;crystals&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:638px;left:162px;white-space:nowrap\" class=\"ft544\">On the&nbsp;basis&nbsp;of optic&nbsp;axes&nbsp;doubly&nbsp;refracting&nbsp;crystals&nbsp;are&nbsp;divided in following&nbsp;two&nbsp;<br \/>categories:-&nbsp;<br \/>&nbsp;<br \/><b>&nbsp; &nbsp;&nbsp;<\/b>&nbsp;<\/p>\n<p style=\"position:absolute;top:740px;left:135px;white-space:nowrap\" class=\"ft540\">1.&nbsp;&nbsp;Uniaxial Cryatals:-&nbsp;There&nbsp;is&nbsp;only&nbsp;one&nbsp;direction called optic&nbsp;axes&nbsp;along&nbsp;which refracted&nbsp;<\/p>\n<p style=\"position:absolute;top:765px;left:162px;white-space:nowrap\" class=\"ft540\">beam travel&nbsp;with&nbsp;same&nbsp;velocity,&nbsp;such&nbsp;as&nbsp;Calcite,&nbsp;Tourmaline&nbsp;crystals.&nbsp;<\/p>\n<p style=\"position:absolute;top:790px;left:135px;white-space:nowrap\" class=\"ft540\">2.&nbsp;&nbsp;&nbsp;Biaxial Crystals:&nbsp;&#8211;&nbsp;There&nbsp;are&nbsp;two&nbsp;directions&nbsp;along&nbsp;which the&nbsp;velocities&nbsp;of refracted beams&nbsp;<\/p>\n<p style=\"position:absolute;top:815px;left:162px;white-space:nowrap\" class=\"ft540\">are&nbsp;same,&nbsp;such&nbsp;as&nbsp;Topaz,&nbsp;Argonite,&nbsp;and&nbsp;Mica.&nbsp;<\/p>\n<p style=\"position:absolute;top:859px;left:135px;white-space:nowrap\" class=\"ft540\">&nbsp;<\/p>\n<\/div>\n<div id=\"page55-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559055.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft550\">31&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft550\">&nbsp;<\/p>\n<p style=\"position:absolute;top:369px;left:729px;white-space:nowrap\" class=\"ft550\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:407px;left:108px;white-space:nowrap\" class=\"ft552\"><b>Calcite&nbsp;Crystal:&nbsp;&#8211;&nbsp;<\/b>It&nbsp;is&nbsp;hydrated&nbsp;calcium carbonate.&nbsp;It&nbsp;is&nbsp;colourless&nbsp;crystal&nbsp;which&nbsp;is&nbsp;transparent&nbsp;for&nbsp;<br \/>visible&nbsp;and ultraviolet light.&nbsp;In&nbsp;nature&nbsp;it is&nbsp;generally&nbsp;found in rhombohedral&nbsp;shape.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:476px;left:108px;white-space:nowrap\" class=\"ft550\">Its&nbsp;each&nbsp;face&nbsp;is&nbsp;a parallelogram with&nbsp;angle&nbsp;102&deg; and&nbsp;78&deg;.&nbsp;At&nbsp;the&nbsp;two&nbsp;diametrically&nbsp;opposite&nbsp;<\/p>\n<p style=\"position:absolute;top:498px;left:108px;white-space:nowrap\" class=\"ft550\">corner&nbsp;three&nbsp;obtuse&nbsp;angle&nbsp;meet.&nbsp;These&nbsp;corners&nbsp;are&nbsp;called blunt corners.&nbsp;At the&nbsp;six&nbsp;remaining&nbsp;<\/p>\n<p style=\"position:absolute;top:520px;left:108px;white-space:nowrap\" class=\"ft550\">corners&nbsp;of the&nbsp;crystal&nbsp;one&nbsp;obtuse&nbsp;and two&nbsp;acute&nbsp;angle&nbsp;meet.&nbsp;The&nbsp;optic&nbsp;axes&nbsp;of the&nbsp;crystal&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:542px;left:108px;white-space:nowrap\" class=\"ft550\">along&nbsp;that line&nbsp;passing&nbsp;through the&nbsp;blunt corners, which makes&nbsp;an equal&nbsp;angle&nbsp;with three&nbsp;faces.&nbsp;<\/p>\n<p style=\"position:absolute;top:564px;left:108px;white-space:nowrap\" class=\"ft551\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:598px;left:116px;white-space:nowrap\" class=\"ft550\">S.NO.&nbsp;&nbsp;RGPV QUESTION&nbsp;<\/p>\n<p style=\"position:absolute;top:598px;left:581px;white-space:nowrap\" class=\"ft550\">YEAR&nbsp;<\/p>\n<p style=\"position:absolute;top:598px;left:702px;white-space:nowrap\" class=\"ft550\">MARKS&nbsp;<\/p>\n<p style=\"position:absolute;top:632px;left:116px;white-space:nowrap\" class=\"ft550\">1&nbsp;<\/p>\n<p style=\"position:absolute;top:632px;left:182px;white-space:nowrap\" class=\"ft553\">For a glass&nbsp;to&nbsp;air the&nbsp;critical angle&nbsp;of&nbsp;refraction&nbsp;is&nbsp;<br \/>40&deg;.&nbsp;Calculate&nbsp;the&nbsp;angle&nbsp;of&nbsp;polarization&nbsp;for glass.&nbsp;<\/p>\n<p style=\"position:absolute;top:632px;left:581px;white-space:nowrap\" class=\"ft550\">June2013&nbsp;<\/p>\n<p style=\"position:absolute;top:632px;left:702px;white-space:nowrap\" class=\"ft550\">4&nbsp;<\/p>\n<p style=\"position:absolute;top:698px;left:116px;white-space:nowrap\" class=\"ft550\">2&nbsp;<\/p>\n<p style=\"position:absolute;top:698px;left:182px;white-space:nowrap\" class=\"ft553\">What is&nbsp;polarization of light?&nbsp;Distinguish between&nbsp;<br \/>plane,&nbsp;circularly&nbsp;and&nbsp;elliptically&nbsp;polarized&nbsp;light.&nbsp;<br \/>Explain&nbsp;the&nbsp;terms&nbsp;plane&nbsp;of&nbsp;polarization&nbsp;and&nbsp;plane&nbsp;of&nbsp;<br \/>vibration.&nbsp;<\/p>\n<p style=\"position:absolute;top:698px;left:581px;white-space:nowrap\" class=\"ft550\">Dec&nbsp;2011&nbsp;<\/p>\n<p style=\"position:absolute;top:698px;left:702px;white-space:nowrap\" class=\"ft550\">14&nbsp;<\/p>\n<p style=\"position:absolute;top:831px;left:108px;white-space:nowrap\" class=\"ft556\"><b>&nbsp;<br \/>&nbsp;<br \/>&nbsp;<br \/>&nbsp;<br \/>&nbsp;<br \/>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:1028px;left:459px;white-space:nowrap\" class=\"ft555\"><b>&nbsp;<br \/>&nbsp;<br \/>&nbsp;<\/b><\/p>\n<\/div>\n<div id=\"page56-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559056.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft560\">32&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft560\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:388px;white-space:nowrap\" class=\"ft561\"><b>Unit-02\/Lecture-12&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:79px;left:108px;white-space:nowrap\" class=\"ft560\">&nbsp;<\/p>\n<p style=\"position:absolute;top:102px;left:108px;white-space:nowrap\" class=\"ft561\"><b>NICOL&nbsp;PRISM:-&nbsp;&nbsp;[RGPV\/Dec2012(4),Dec2013(4)]&nbsp;&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:142px;left:108px;white-space:nowrap\" class=\"ft560\">It&nbsp;is&nbsp;a special kind&nbsp;of&nbsp;prism made&nbsp;up&nbsp;of&nbsp;natural calcite&nbsp;crystal&nbsp;which&nbsp;is&nbsp;used&nbsp;to&nbsp;obtain&nbsp;plane&nbsp;<\/p>\n<p style=\"position:absolute;top:164px;left:108px;white-space:nowrap\" class=\"ft560\">polarized&nbsp;light&nbsp;from unpolarized&nbsp;light&nbsp;and&nbsp;also&nbsp;used&nbsp;for the&nbsp;analysis&nbsp;of&nbsp;given&nbsp;light.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:204px;left:108px;white-space:nowrap\" class=\"ft560\">Nicol prism is&nbsp;constructed&nbsp;from a calcite&nbsp;crystal&nbsp;whose&nbsp;length&nbsp;is&nbsp;nearly&nbsp;3&nbsp;times&nbsp;of its&nbsp;width.&nbsp;The&nbsp;<\/p>\n<p style=\"position:absolute;top:226px;left:108px;white-space:nowrap\" class=\"ft560\">end faces&nbsp;of crystal&nbsp;are&nbsp;cut down to&nbsp;reduce&nbsp;the&nbsp;angle&nbsp;in principle&nbsp;section to&nbsp;more&nbsp;acute&nbsp;angle&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:248px;left:108px;white-space:nowrap\" class=\"ft560\">68&deg;&nbsp;instead of 78&deg;.&nbsp;The&nbsp;crystal&nbsp;is&nbsp;then cut along&nbsp;the&nbsp;diagonal&nbsp;and two&nbsp;cut&nbsp;surfaces&nbsp;are&nbsp;after&nbsp;<\/p>\n<p style=\"position:absolute;top:270px;left:108px;white-space:nowrap\" class=\"ft560\">polishing, are&nbsp;cemented&nbsp;back together&nbsp;with&nbsp;special cement&nbsp;called&nbsp;Canada Balsam,&nbsp;which&nbsp;is&nbsp;a&nbsp;<\/p>\n<p style=\"position:absolute;top:292px;left:108px;white-space:nowrap\" class=\"ft560\">transparent substance.&nbsp;It is&nbsp;optically&nbsp;denser&nbsp;than&nbsp;Calcite&nbsp;for&nbsp;the&nbsp;extraordinary&nbsp;ray&nbsp;and&nbsp;less&nbsp;dense&nbsp;<\/p>\n<p style=\"position:absolute;top:314px;left:108px;white-space:nowrap\" class=\"ft560\">for ordinary&nbsp;rays.&nbsp;<\/p>\n<p style=\"position:absolute;top:353px;left:108px;white-space:nowrap\" class=\"ft561\"><b>Working: &nbsp;<\/b>&nbsp;&nbsp;A&nbsp;ray&nbsp;of light is&nbsp;incident on the&nbsp;surface&nbsp;of the&nbsp;Nicol&nbsp;prism&nbsp;splits&nbsp;into&nbsp;E-ray&nbsp;and&nbsp;O-ray&nbsp;<\/p>\n<p style=\"position:absolute;top:375px;left:108px;white-space:nowrap\" class=\"ft560\">whose&nbsp;vibrations&nbsp;are&nbsp;respectively&nbsp;perpendicular&nbsp;and parallel&nbsp;to&nbsp;the&nbsp;principle&nbsp;section of Nicol&nbsp;<\/p>\n<p style=\"position:absolute;top:397px;left:108px;white-space:nowrap\" class=\"ft560\">prism.&nbsp;The&nbsp;O-ray&nbsp;suffers&nbsp;total internal reflection&nbsp;at&nbsp;the&nbsp;Canada Balsam,&nbsp;surface&nbsp;for nearly&nbsp;normal&nbsp;<\/p>\n<p style=\"position:absolute;top:419px;left:108px;white-space:nowrap\" class=\"ft560\">incidence&nbsp;because&nbsp;Canada Balsam is&nbsp;optically&nbsp;less dense&nbsp;for&nbsp;O-ray,&nbsp;while&nbsp;E-&nbsp;ray&nbsp;suffers&nbsp;refraction&nbsp;<\/p>\n<p style=\"position:absolute;top:441px;left:108px;white-space:nowrap\" class=\"ft560\">at&nbsp;Canada Balsam surface&nbsp;as&nbsp;Canada&nbsp;Balsam is&nbsp;denser than&nbsp;calcite&nbsp;for E-&nbsp;ray.&nbsp;<\/p>\n<p style=\"position:absolute;top:802px;left:657px;white-space:nowrap\" class=\"ft561\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:848px;left:108px;white-space:nowrap\" class=\"ft561\"><b>Use&nbsp;of&nbsp;Nicol&nbsp;Prism&nbsp;as Polarizer&nbsp;and&nbsp;Analyzer&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:888px;left:108px;white-space:nowrap\" class=\"ft560\">When&nbsp;two&nbsp;Nicol Prisms&nbsp;are&nbsp;arranged&nbsp;coaxially&nbsp;than&nbsp;the&nbsp;first&nbsp;Nicole&nbsp;Prism which&nbsp;produces&nbsp;plane&nbsp;<\/p>\n<p style=\"position:absolute;top:910px;left:108px;white-space:nowrap\" class=\"ft560\">polarized&nbsp;light&nbsp;is&nbsp;known&nbsp;as&nbsp;Polarizer&nbsp;while&nbsp;the&nbsp;second&nbsp;which&nbsp;analyses&nbsp;the&nbsp;polarized&nbsp;light&nbsp;is&nbsp;<\/p>\n<p style=\"position:absolute;top:932px;left:108px;white-space:nowrap\" class=\"ft560\">known as&nbsp;analyzer.&nbsp;When the&nbsp;two&nbsp;Nicol&nbsp;prisms&nbsp;are&nbsp;placed with their&nbsp;principle&nbsp;sections&nbsp;parallel&nbsp;<\/p>\n<p style=\"position:absolute;top:954px;left:108px;white-space:nowrap\" class=\"ft560\">to&nbsp;each other, then the&nbsp;extraordinary&nbsp;ray&nbsp;transmitted&nbsp;by one is&nbsp;freely transmitted&nbsp;by the other.&nbsp;<\/p>\n<p style=\"position:absolute;top:976px;left:108px;white-space:nowrap\" class=\"ft560\">If the&nbsp;second prism&nbsp;is&nbsp;gradually&nbsp;rotated, then the&nbsp;intensity&nbsp;of extraordinary&nbsp;ray&nbsp;gradually&nbsp;<\/p>\n<p style=\"position:absolute;top:998px;left:108px;white-space:nowrap\" class=\"ft560\">decreases&nbsp;and when the&nbsp;two&nbsp;Nicol&nbsp;prisms&nbsp;are&nbsp;at right angle&nbsp;to&nbsp;each other&nbsp;i.e&nbsp;they&nbsp;are&nbsp;in crossed&nbsp;<\/p>\n<p style=\"position:absolute;top:1020px;left:108px;white-space:nowrap\" class=\"ft560\">position,&nbsp;no&nbsp;light&nbsp;comes&nbsp;from&nbsp;second prism.&nbsp;This&nbsp;is&nbsp;due&nbsp;to&nbsp;the&nbsp;fact that when the&nbsp;polarized&nbsp;<\/p>\n<p style=\"position:absolute;top:1042px;left:108px;white-space:nowrap\" class=\"ft560\">extraordinary&nbsp;ray&nbsp;enters&nbsp;the&nbsp;second&nbsp;Nicole&nbsp;prism,&nbsp;it&nbsp;acts&nbsp;as&nbsp;ordinary&nbsp;ray&nbsp;and&nbsp;totally&nbsp;internally&nbsp;<\/p>\n<p style=\"position:absolute;top:1064px;left:108px;white-space:nowrap\" class=\"ft560\">reflected.&nbsp;Therefore, the&nbsp;first Nicol&nbsp;prism&nbsp;produces&nbsp;plane&nbsp;polarized light and the&nbsp;second&nbsp;Nicol&nbsp;<\/p>\n<p style=\"position:absolute;top:1086px;left:108px;white-space:nowrap\" class=\"ft560\">prism analyses&nbsp;the&nbsp;light.&nbsp;&nbsp;<\/p>\n<\/div>\n<div id=\"page57-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559057.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft570\">33&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft570\">&nbsp;<\/p>\n<p style=\"position:absolute;top:64px;left:108px;white-space:nowrap\" class=\"ft570\">If a&nbsp;given light is&nbsp;examined through rotating&nbsp;Nicol&nbsp;prism&nbsp;and it shows&nbsp;a&nbsp;variation in intensity&nbsp;with&nbsp;<\/p>\n<p style=\"position:absolute;top:86px;left:108px;white-space:nowrap\" class=\"ft570\">minimum intensity&nbsp;zero,&nbsp;the&nbsp;given&nbsp;light&nbsp;is&nbsp;plane&nbsp;polarized,&nbsp;and&nbsp;if&nbsp;intensity&nbsp;does&nbsp;not&nbsp;fall to&nbsp;zero&nbsp;<\/p>\n<p style=\"position:absolute;top:108px;left:108px;white-space:nowrap\" class=\"ft570\">than the&nbsp;light is&nbsp;unpolarized&nbsp;light.&nbsp;<\/p>\n<p style=\"position:absolute;top:148px;left:162px;white-space:nowrap\" class=\"ft570\">&nbsp;<\/p>\n<p style=\"position:absolute;top:188px;left:108px;white-space:nowrap\" class=\"ft571\"><b>Retardation&nbsp;Plates&nbsp;&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:228px;left:162px;white-space:nowrap\" class=\"ft571\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:268px;left:108px;white-space:nowrap\" class=\"ft570\">The&nbsp;crystal&nbsp;plates&nbsp;of doubly&nbsp;refracting&nbsp;crystal&nbsp;that retards&nbsp;the&nbsp;motion of&nbsp;one&nbsp;of the&nbsp;refracted&nbsp;<\/p>\n<p style=\"position:absolute;top:290px;left:108px;white-space:nowrap\" class=\"ft570\">beams&nbsp;(O-ray&nbsp;and&nbsp;E-ray)&nbsp;are&nbsp;known as&nbsp;retardation plates.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:330px;left:108px;white-space:nowrap\" class=\"ft570\">These&nbsp;are&nbsp;of two&nbsp;types:&nbsp;<\/p>\n<p style=\"position:absolute;top:352px;left:108px;white-space:nowrap\" class=\"ft571\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:374px;left:108px;white-space:nowrap\" class=\"ft571\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:414px;left:176px;white-space:nowrap\" class=\"ft578\">1.&nbsp;&nbsp;Half&nbsp;wave Plate&nbsp;&nbsp;<br \/>2.&nbsp;&nbsp;Quarter wave&nbsp;Plate&nbsp;<\/p>\n<p style=\"position:absolute;top:464px;left:189px;white-space:nowrap\" class=\"ft570\">&nbsp;<\/p>\n<p style=\"position:absolute;top:504px;left:108px;white-space:nowrap\" class=\"ft571\"><b>Half wave&nbsp;Plate&nbsp;:&nbsp;<\/b>&nbsp;It is&nbsp;a&nbsp;crystal&nbsp;of plate&nbsp;of doubly&nbsp;refracting&nbsp;material&nbsp;whose&nbsp;thickness&nbsp;is&nbsp;such&nbsp;<\/p>\n<p style=\"position:absolute;top:526px;left:108px;white-space:nowrap\" class=\"ft570\">that&nbsp;it&nbsp;introduces&nbsp;a&nbsp;phase&nbsp;difference&nbsp;of&nbsp;&pi;&nbsp;or&nbsp;path&nbsp;difference&nbsp;of&nbsp;&lambda;\/2&nbsp;between&nbsp;the&nbsp;ordinary&nbsp;ray&nbsp;and&nbsp;<\/p>\n<p style=\"position:absolute;top:548px;left:108px;white-space:nowrap\" class=\"ft570\">extraordinary&nbsp;ray&nbsp; than&nbsp;it&nbsp;is&nbsp;called&nbsp;half&nbsp;wave&nbsp;plate.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:597px;left:162px;white-space:nowrap\" class=\"ft570\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;<\/p>\n<p style=\"position:absolute;top:596px;left:309px;white-space:nowrap\" class=\"ft572\">&#119905;&#119905;&nbsp;=<\/p>\n<p style=\"position:absolute;top:589px;left:363px;white-space:nowrap\" class=\"ft573\">&#120582;&#120582;<\/p>\n<p style=\"position:absolute;top:612px;left:345px;white-space:nowrap\" class=\"ft573\">2&nbsp;(&#9651;<i>&micro;<\/i>)<\/p>\n<p style=\"position:absolute;top:594px;left:390px;white-space:nowrap\" class=\"ft572\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:646px;left:108px;white-space:nowrap\" class=\"ft570\">Where&nbsp;t is&nbsp;thickness&nbsp;of plate, &nbsp;&#9651;= &micro;<\/p>\n<p style=\"position:absolute;top:655px;left:365px;white-space:nowrap\" class=\"ft575\">e<\/p>\n<p style=\"position:absolute;top:646px;left:371px;white-space:nowrap\" class=\"ft570\">-&micro;<\/p>\n<p style=\"position:absolute;top:655px;left:387px;white-space:nowrap\" class=\"ft575\">o&nbsp;<\/p>\n<p style=\"position:absolute;top:646px;left:396px;white-space:nowrap\" class=\"ft570\">or&nbsp;&#9651;= &micro;<\/p>\n<p style=\"position:absolute;top:655px;left:453px;white-space:nowrap\" class=\"ft575\">o<\/p>\n<p style=\"position:absolute;top:646px;left:460px;white-space:nowrap\" class=\"ft570\">-&micro;<\/p>\n<p style=\"position:absolute;top:655px;left:475px;white-space:nowrap\" class=\"ft575\">e<\/p>\n<p style=\"position:absolute;top:646px;left:481px;white-space:nowrap\" class=\"ft570\">&nbsp;<\/p>\n<p style=\"position:absolute;top:686px;left:162px;white-space:nowrap\" class=\"ft570\">&nbsp;<\/p>\n<p style=\"position:absolute;top:726px;left:108px;white-space:nowrap\" class=\"ft571\"><b>Quarter&nbsp;wave&nbsp;Plate&nbsp;:&nbsp;<\/b>&nbsp;It&nbsp;is&nbsp;a&nbsp;crystal&nbsp;of plate&nbsp;of doubly&nbsp;refracting&nbsp;material&nbsp;whose&nbsp;thickness&nbsp;is&nbsp;such&nbsp;<\/p>\n<p style=\"position:absolute;top:748px;left:108px;white-space:nowrap\" class=\"ft570\">that&nbsp;it&nbsp;introduces&nbsp;a&nbsp;phase&nbsp;difference&nbsp;of&nbsp;&pi;&nbsp;\/2or&nbsp;path&nbsp;difference&nbsp;of&nbsp;&lambda;\/4between&nbsp;the&nbsp;ordinary&nbsp;ray&nbsp;<\/p>\n<p style=\"position:absolute;top:770px;left:108px;white-space:nowrap\" class=\"ft570\">and&nbsp;extraordinary&nbsp;ray&nbsp; than&nbsp;it&nbsp;is&nbsp;called&nbsp;half&nbsp;wave&nbsp;plate.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:810px;left:162px;white-space:nowrap\" class=\"ft571\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:832px;left:162px;white-space:nowrap\" class=\"ft579\"><b>&nbsp;<br \/>&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;<\/b>&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&#119905;&#119905;&nbsp;=<\/p>\n<p style=\"position:absolute;top:855px;left:447px;white-space:nowrap\" class=\"ft576\">&#120582;&#120582;<\/p>\n<p style=\"position:absolute;top:875px;left:433px;white-space:nowrap\" class=\"ft576\">4(&#9651;<i>&micro;<\/i>)<\/p>\n<p style=\"position:absolute;top:859px;left:469px;white-space:nowrap\" class=\"ft570\">&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:907px;left:108px;white-space:nowrap\" class=\"ft570\">Where&nbsp;t is&nbsp;thickness&nbsp;of plate,&nbsp;&nbsp;&#9651;=&nbsp;&micro;<\/p>\n<p style=\"position:absolute;top:916px;left:380px;white-space:nowrap\" class=\"ft575\">e<\/p>\n<p style=\"position:absolute;top:907px;left:386px;white-space:nowrap\" class=\"ft570\">-&micro;<\/p>\n<p style=\"position:absolute;top:916px;left:401px;white-space:nowrap\" class=\"ft575\">o&nbsp;<\/p>\n<p style=\"position:absolute;top:907px;left:410px;white-space:nowrap\" class=\"ft570\">or&nbsp;&#9651;= &micro;<\/p>\n<p style=\"position:absolute;top:916px;left:468px;white-space:nowrap\" class=\"ft575\">o<\/p>\n<p style=\"position:absolute;top:907px;left:475px;white-space:nowrap\" class=\"ft570\">-&micro;<\/p>\n<p style=\"position:absolute;top:916px;left:490px;white-space:nowrap\" class=\"ft575\">e<\/p>\n<p style=\"position:absolute;top:907px;left:496px;white-space:nowrap\" class=\"ft570\">&nbsp;<\/p>\n<p style=\"position:absolute;top:948px;left:162px;white-space:nowrap\" class=\"ft570\">&nbsp;<\/p>\n<p style=\"position:absolute;top:970px;left:170px;white-space:nowrap\" class=\"ft570\">S.No.&nbsp;<\/p>\n<p style=\"position:absolute;top:970px;left:385px;white-space:nowrap\" class=\"ft570\">Question&nbsp;<\/p>\n<p style=\"position:absolute;top:970px;left:628px;white-space:nowrap\" class=\"ft570\">year&nbsp;<\/p>\n<p style=\"position:absolute;top:970px;left:716px;white-space:nowrap\" class=\"ft570\">Marks&nbsp;<\/p>\n<p style=\"position:absolute;top:1011px;left:170px;white-space:nowrap\" class=\"ft570\">1&nbsp;<\/p>\n<p style=\"position:absolute;top:993px;left:225px;white-space:nowrap\" class=\"ft570\">Discuss&nbsp;working&nbsp;of&nbsp;Nicol&nbsp;prism as&nbsp;Polarizer and&nbsp;<\/p>\n<p style=\"position:absolute;top:1015px;left:225px;white-space:nowrap\" class=\"ft570\">Analyzer.&nbsp;<\/p>\n<p style=\"position:absolute;top:993px;left:628px;white-space:nowrap\" class=\"ft570\">Dec&nbsp;2013&nbsp;&nbsp;7&nbsp;<\/p>\n<p style=\"position:absolute;top:1056px;left:170px;white-space:nowrap\" class=\"ft570\">2&nbsp;<\/p>\n<p style=\"position:absolute;top:1038px;left:225px;white-space:nowrap\" class=\"ft570\">For a calcite,&nbsp;&micro;<\/p>\n<p style=\"position:absolute;top:1046px;left:331px;white-space:nowrap\" class=\"ft575\">o<\/p>\n<p style=\"position:absolute;top:1038px;left:337px;white-space:nowrap\" class=\"ft570\">=1.658and&nbsp;&micro;<\/p>\n<p style=\"position:absolute;top:1046px;left:429px;white-space:nowrap\" class=\"ft575\">e<\/p>\n<p style=\"position:absolute;top:1038px;left:435px;white-space:nowrap\" class=\"ft570\">=1.486 for&nbsp;sodium&nbsp;light&nbsp;<\/p>\n<p style=\"position:absolute;top:1060px;left:225px;white-space:nowrap\" class=\"ft570\">Of&nbsp;&lambda;=5893A&deg;.&nbsp;Calculate&nbsp;the&nbsp;minimum&nbsp;thickness&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:1082px;left:225px;white-space:nowrap\" class=\"ft570\">quarter wave&nbsp;plate&nbsp;for calcite.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:1038px;left:628px;white-space:nowrap\" class=\"ft570\">Dec&nbsp;2012&nbsp;&nbsp;4&nbsp;<\/p>\n<p style=\"position:absolute;top:1104px;left:100px;white-space:nowrap\" class=\"ft571\"><b>&nbsp; &nbsp;<\/b>&nbsp;<\/p>\n<\/div>\n<div id=\"page58-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559058.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft580\">34&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft580\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:100px;white-space:nowrap\" class=\"ft580\">&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:68px;left:810px;white-space:nowrap\" class=\"ft580\">&nbsp;<\/p>\n<p style=\"position:absolute;top:90px;left:388px;white-space:nowrap\" class=\"ft581\"><b>Unit-02\/Lecture-13&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:123px;left:108px;white-space:nowrap\" class=\"ft580\">&nbsp;<\/p>\n<p style=\"position:absolute;top:146px;left:108px;white-space:nowrap\" class=\"ft582\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:166px;left:108px;white-space:nowrap\" class=\"ft582\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:186px;left:162px;white-space:nowrap\" class=\"ft580\">1.&nbsp;&nbsp;The&nbsp;distance&nbsp;between the&nbsp;slit and biprism&nbsp;and between biprism&nbsp;and screen are&nbsp;50&nbsp;<\/p>\n<p style=\"position:absolute;top:211px;left:189px;white-space:nowrap\" class=\"ft584\">cm each.&nbsp;The&nbsp;angle&nbsp;of&nbsp;biprism is&nbsp;179&deg;and its&nbsp;refractive&nbsp;index&nbsp;is&nbsp;1.5.&nbsp;If the&nbsp;distance&nbsp;<br \/>between&nbsp;successive fringes&nbsp;is&nbsp;0.0135cm,&nbsp;calculate the wavelength&nbsp;of&nbsp;light.&nbsp;<\/p>\n<p style=\"position:absolute;top:262px;left:162px;white-space:nowrap\" class=\"ft580\">2.&nbsp;&nbsp;In&nbsp;a biprism&nbsp;experiment&nbsp;the&nbsp;distance&nbsp;between&nbsp;slit&nbsp;and&nbsp;screen&nbsp;is&nbsp;160cm.The&nbsp;biprism is&nbsp;<\/p>\n<p style=\"position:absolute;top:287px;left:189px;white-space:nowrap\" class=\"ft584\">40&nbsp;cm&nbsp;away&nbsp;from&nbsp;the&nbsp;slit and its&nbsp;refractive&nbsp;index&nbsp;is&nbsp;1.52.&nbsp;When a&nbsp;source&nbsp;of&nbsp;<br \/>wavelength 5893A&nbsp;is&nbsp;used the&nbsp;fringe&nbsp;width is&nbsp;found to&nbsp;be&nbsp;0.01&nbsp;cm.&nbsp;Find the&nbsp;angle&nbsp;of&nbsp;<br \/>prism.&nbsp;<\/p>\n<p style=\"position:absolute;top:363px;left:162px;white-space:nowrap\" class=\"ft580\">3.&nbsp;&nbsp;A&nbsp;parallel&nbsp;beam&nbsp;of&nbsp;light&nbsp;&lambda;=&nbsp;5890A&nbsp;is&nbsp;incident&nbsp;on&nbsp;a&nbsp;thin&nbsp;glass plate&nbsp;&micro;=1.5&nbsp;such&nbsp;that&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:388px;left:189px;white-space:nowrap\" class=\"ft584\">angle&nbsp;of refraction into&nbsp;the&nbsp;plate&nbsp;is&nbsp;60&deg;.&nbsp;Calculate&nbsp;the&nbsp;smallest thickness&nbsp;of the&nbsp;glass&nbsp;<br \/>plate&nbsp;which&nbsp;will&nbsp;appear&nbsp;dark by&nbsp;reflection.&nbsp;<\/p>\n<p style=\"position:absolute;top:439px;left:162px;white-space:nowrap\" class=\"ft580\">4.&nbsp;&nbsp;In Newton&rsquo;s&nbsp;rings&nbsp;experiment the&nbsp;diameter&nbsp;of the&nbsp;10<\/p>\n<p style=\"position:absolute;top:436px;left:572px;white-space:nowrap\" class=\"ft583\">th<\/p>\n<p style=\"position:absolute;top:439px;left:582px;white-space:nowrap\" class=\"ft580\">&nbsp;dark&nbsp;ring&nbsp;is&nbsp;0.433cm.&nbsp;Find&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:464px;left:189px;white-space:nowrap\" class=\"ft580\">wavelength of incident light, if the&nbsp;radius&nbsp;of curvature&nbsp;of the&nbsp;lens&nbsp;is&nbsp;70cm.&nbsp;<\/p>\n<p style=\"position:absolute;top:489px;left:162px;white-space:nowrap\" class=\"ft580\">5.&nbsp;&nbsp;A&nbsp;Newton&rsquo;s&nbsp;rings&nbsp;arrangement is&nbsp;used with a&nbsp;source&nbsp;emitting&nbsp;two&nbsp;wavelengths&nbsp;<\/p>\n<p style=\"position:absolute;top:514px;left:189px;white-space:nowrap\" class=\"ft580\">&lambda;1=6000A&nbsp;and&nbsp;&lambda;2=4500A&nbsp;and&nbsp;it&nbsp;is&nbsp;found&nbsp;that&nbsp;n<\/p>\n<p style=\"position:absolute;top:512px;left:527px;white-space:nowrap\" class=\"ft583\">th<\/p>\n<p style=\"position:absolute;top:514px;left:537px;white-space:nowrap\" class=\"ft580\">&nbsp;dark&nbsp;ring&nbsp;due&nbsp;to&nbsp;&lambda;1&nbsp;coincides&nbsp;with&nbsp;<\/p>\n<p style=\"position:absolute;top:540px;left:189px;white-space:nowrap\" class=\"ft584\">the&nbsp;(n+1)th&nbsp;dark&nbsp;ring&nbsp;of&nbsp;&lambda;2.&nbsp;If&nbsp;radius&nbsp;of&nbsp;curvature&nbsp;of&nbsp;curved&nbsp;surface&nbsp;is&nbsp;90cm&nbsp;,&nbsp;find&nbsp;the&nbsp;<br \/>diameter&nbsp;of&nbsp;nth&nbsp;dark&nbsp;ring&nbsp;for&nbsp;&lambda;1.&nbsp;<\/p>\n<p style=\"position:absolute;top:563px;left:427px;white-space:nowrap\" class=\"ft583\">&nbsp;<\/p>\n<p style=\"position:absolute;top:565px;left:430px;white-space:nowrap\" class=\"ft580\">&nbsp;<\/p>\n<p style=\"position:absolute;top:590px;left:162px;white-space:nowrap\" class=\"ft580\">6.&nbsp;&nbsp;Newton&rsquo;s&nbsp;rings&nbsp;are&nbsp;observed&nbsp;by&nbsp;keeping&nbsp;a spherical surface&nbsp;of&nbsp;100cm radius&nbsp;on&nbsp;a&nbsp;<\/p>\n<p style=\"position:absolute;top:615px;left:189px;white-space:nowrap\" class=\"ft580\">plane&nbsp;glass&nbsp;plate.&nbsp;If the&nbsp;diameter&nbsp;of the&nbsp;16<\/p>\n<p style=\"position:absolute;top:613px;left:497px;white-space:nowrap\" class=\"ft583\">th<\/p>\n<p style=\"position:absolute;top:615px;left:508px;white-space:nowrap\" class=\"ft580\">&nbsp;bright ring&nbsp;is0.590cm&nbsp;what is&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:641px;left:189px;white-space:nowrap\" class=\"ft580\">wavelength if light used.&nbsp;<\/p>\n<p style=\"position:absolute;top:666px;left:162px;white-space:nowrap\" class=\"ft580\">7.&nbsp;&nbsp;&nbsp;In Newton&rsquo;s&nbsp;rings&nbsp;experiment, the&nbsp;diameter&nbsp;of the&nbsp;4<\/p>\n<p style=\"position:absolute;top:664px;left:572px;white-space:nowrap\" class=\"ft583\">th<\/p>\n<p style=\"position:absolute;top:666px;left:582px;white-space:nowrap\" class=\"ft580\">&nbsp;and 12<\/p>\n<p style=\"position:absolute;top:664px;left:636px;white-space:nowrap\" class=\"ft583\">th<\/p>\n<p style=\"position:absolute;top:666px;left:646px;white-space:nowrap\" class=\"ft580\">&nbsp;dark&nbsp;rings&nbsp;is&nbsp;0.400cm&nbsp;<\/p>\n<p style=\"position:absolute;top:691px;left:189px;white-space:nowrap\" class=\"ft580\">and 0.700cm&nbsp;respectively.&nbsp;Find the&nbsp;diameter&nbsp;of 20<\/p>\n<p style=\"position:absolute;top:689px;left:554px;white-space:nowrap\" class=\"ft583\">th<\/p>\n<p style=\"position:absolute;top:691px;left:565px;white-space:nowrap\" class=\"ft580\">&nbsp;dark&nbsp;ring.&nbsp;<\/p>\n<p style=\"position:absolute;top:717px;left:162px;white-space:nowrap\" class=\"ft580\">8.&nbsp;&nbsp;Newton&rsquo;s&nbsp;rings&nbsp;are&nbsp;formed in reflected light of wavelength 6000a&nbsp;with a&nbsp;liquid&nbsp;<\/p>\n<p style=\"position:absolute;top:742px;left:189px;white-space:nowrap\" class=\"ft580\">between the&nbsp;plane&nbsp;and&nbsp;curved surfaces.&nbsp;If the&nbsp;diameter&nbsp;of 6<\/p>\n<p style=\"position:absolute;top:740px;left:626px;white-space:nowrap\" class=\"ft583\">th<\/p>\n<p style=\"position:absolute;top:742px;left:637px;white-space:nowrap\" class=\"ft580\">&nbsp;bright&nbsp;ring&nbsp;is&nbsp;3.1mm&nbsp;<\/p>\n<p style=\"position:absolute;top:767px;left:189px;white-space:nowrap\" class=\"ft584\">and radius&nbsp;of curvature&nbsp;of the&nbsp;curved surface&nbsp;is&nbsp;100cm&nbsp;calculate&nbsp;the&nbsp;refractive&nbsp;index&nbsp;<br \/>of the&nbsp;liquid.&nbsp;<\/p>\n<p style=\"position:absolute;top:818px;left:162px;white-space:nowrap\" class=\"ft580\">9.&nbsp;&nbsp;In a&nbsp;Newton&rsquo;s&nbsp;ring&nbsp;experiment the&nbsp;diameter&nbsp;of 10<\/p>\n<p style=\"position:absolute;top:816px;left:549px;white-space:nowrap\" class=\"ft583\">th<\/p>\n<p style=\"position:absolute;top:818px;left:560px;white-space:nowrap\" class=\"ft580\">&nbsp;ring&nbsp;changes&nbsp;from 1.40cm to&nbsp;<\/p>\n<p style=\"position:absolute;top:843px;left:189px;white-space:nowrap\" class=\"ft584\">1.27cm&nbsp;when a&nbsp;liquid is&nbsp;introduced between the&nbsp;lens&nbsp;and plate.&nbsp;Calculate&nbsp;the&nbsp;<br \/>refractive&nbsp;index&nbsp;of the&nbsp;liquid.&nbsp;<\/p>\n<p style=\"position:absolute;top:893px;left:162px;white-space:nowrap\" class=\"ft580\">10.&nbsp;The&nbsp;movable&nbsp;mirror of&nbsp;Michelson&rsquo;s&nbsp;interferometer is&nbsp;moved&nbsp;through&nbsp;a distance&nbsp;of&nbsp;<\/p>\n<p style=\"position:absolute;top:919px;left:189px;white-space:nowrap\" class=\"ft584\">0.02603mm.&nbsp;Find the&nbsp;number&nbsp;of fringes&nbsp;shifted across&nbsp;the&nbsp;cross-wire of&nbsp;the eyepiece&nbsp;<br \/>of the&nbsp;telescope.&nbsp;If the&nbsp;wavelength of 5206Ais&nbsp;used.&nbsp;<\/p>\n<p style=\"position:absolute;top:969px;left:162px;white-space:nowrap\" class=\"ft580\">11.&nbsp;Calculate&nbsp;the&nbsp;distance&nbsp;between&nbsp;two&nbsp;successive&nbsp;positions&nbsp;of&nbsp;a&nbsp;movable&nbsp;mirror of&nbsp;a&nbsp;<\/p>\n<p style=\"position:absolute;top:994px;left:189px;white-space:nowrap\" class=\"ft584\">Michelson&rsquo;s&nbsp;interferometer giving&nbsp;best fringes&nbsp;in&nbsp;the&nbsp;case&nbsp;of sodium&nbsp;having&nbsp;lines&nbsp;of&nbsp;<br \/>wavelength&nbsp;5890A&nbsp;and&nbsp;5896A.&nbsp;<\/p>\n<p style=\"position:absolute;top:1045px;left:162px;white-space:nowrap\" class=\"ft580\">12.&nbsp;Light of wavelength 5500A&nbsp;falls&nbsp;normally&nbsp;on a&nbsp;slit of width 22000A. Calculate&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:1070px;left:189px;white-space:nowrap\" class=\"ft580\">angular position&nbsp;of&nbsp;first&nbsp;two&nbsp;minima on&nbsp;either side&nbsp;of&nbsp;central&nbsp;maxima.&nbsp;<\/p>\n<p style=\"position:absolute;top:1096px;left:162px;white-space:nowrap\" class=\"ft580\">13.&nbsp;In a&nbsp;double&nbsp;slit diffraction pattern the&nbsp;screen is&nbsp;placed 170cm&nbsp;away&nbsp;from&nbsp;slit.&nbsp;The&nbsp;<\/p>\n<\/div>\n<div id=\"page59-div\" style=\"position:relative;width:918px;height:1188px;\" class=\"kk_zoom\">\n<img width=\"918\" height=\"1188\" src=\"https:\/\/content.kopykitab.com\/pdftohtml\/01c536e431c4f99277130978b38461bf2559059.png\" alt=\"background image\"><\/p>\n<p style=\"position:absolute;top:3px;left:450px;white-space:nowrap\" class=\"ft590\">35&nbsp;<\/p>\n<p style=\"position:absolute;top:26px;left:108px;white-space:nowrap\" class=\"ft590\">&nbsp;<\/p>\n<p style=\"position:absolute;top:46px;left:189px;white-space:nowrap\" class=\"ft592\">width of the&nbsp;slits&nbsp;is&nbsp;0.08mm&nbsp;and they&nbsp;are&nbsp;0.4mm&nbsp;apart.&nbsp;Calculate&nbsp;the&nbsp;wavelength of&nbsp;<br \/>light if the&nbsp;fringe&nbsp;width is&nbsp;0.25cm.&nbsp;Also&nbsp;find the&nbsp;missing&nbsp;order.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:97px;left:162px;white-space:nowrap\" class=\"ft590\">14.&nbsp;How&nbsp;many&nbsp;lines&nbsp;are&nbsp;there&nbsp;on a&nbsp;grating&nbsp;if the&nbsp;angle&nbsp;of diffraction is&nbsp;20&deg;&nbsp;for&nbsp;the&nbsp;first&nbsp;<\/p>\n<p style=\"position:absolute;top:122px;left:189px;white-space:nowrap\" class=\"ft590\">order, when light of wavelength 600nm&nbsp;is&nbsp;incident on the&nbsp;grating&nbsp;normally.&nbsp;<\/p>\n<p style=\"position:absolute;top:147px;left:162px;white-space:nowrap\" class=\"ft590\">15.&nbsp;How many&nbsp;orders&nbsp;will&nbsp;be&nbsp;visible&nbsp;if the&nbsp;wavelength of the&nbsp;incident radiation is&nbsp;5000A&nbsp;<\/p>\n<p style=\"position:absolute;top:172px;left:189px;white-space:nowrap\" class=\"ft590\">and the&nbsp;number&nbsp;of lines&nbsp;on the&nbsp;grating&nbsp;is&nbsp;2620in&nbsp;one&nbsp;inch?&nbsp;<\/p>\n<p style=\"position:absolute;top:198px;left:162px;white-space:nowrap\" class=\"ft590\">16.&nbsp;In a&nbsp;fraunhoffer&nbsp;diffraction pattern of a&nbsp;n slit , it is&nbsp;found that&nbsp;the&nbsp;forth secondary&nbsp;<\/p>\n<p style=\"position:absolute;top:223px;left:189px;white-space:nowrap\" class=\"ft590\">maxima&nbsp;is&nbsp;missing.&nbsp;What&nbsp;is&nbsp;the&nbsp;ratio&nbsp;of the&nbsp;slit width to&nbsp;the&nbsp;slit separation?&nbsp;<\/p>\n<p style=\"position:absolute;top:248px;left:162px;white-space:nowrap\" class=\"ft590\">17.&nbsp;If&nbsp;two&nbsp;spectral&nbsp;lines&nbsp;of&nbsp;wavelength&nbsp;5890A&nbsp;and&nbsp;5896A&nbsp;are&nbsp;to be&nbsp;seen just separated in&nbsp;<\/p>\n<p style=\"position:absolute;top:273px;left:189px;white-space:nowrap\" class=\"ft590\">the&nbsp;first order&nbsp;spectrum&nbsp;of the&nbsp;grating, find the&nbsp;number&nbsp;of lines&nbsp;in the&nbsp;grating.&nbsp;<\/p>\n<p style=\"position:absolute;top:299px;left:162px;white-space:nowrap\" class=\"ft590\">18.&nbsp;A&nbsp;grating&nbsp;has&nbsp;15cm&nbsp;of the&nbsp;surface&nbsp;ruled with 6000&nbsp;lines&nbsp;per&nbsp;cm&nbsp;what is&nbsp;the&nbsp;resolving&nbsp;<\/p>\n<p style=\"position:absolute;top:324px;left:189px;white-space:nowrap\" class=\"ft590\">power&nbsp;of grating&nbsp;in the&nbsp;first order.&nbsp;<\/p>\n<p style=\"position:absolute;top:349px;left:162px;white-space:nowrap\" class=\"ft590\">19.&nbsp;What must be&nbsp;minimum&nbsp;number&nbsp;of lines&nbsp;per&nbsp;cm&nbsp;in a&nbsp;half inch width grating&nbsp;to&nbsp;<\/p>\n<p style=\"position:absolute;top:374px;left:189px;white-space:nowrap\" class=\"ft590\">resolve&nbsp;the&nbsp;D1&nbsp;and D2&nbsp;lines&nbsp;of sodium.&nbsp;<\/p>\n<p style=\"position:absolute;top:400px;left:162px;white-space:nowrap\" class=\"ft590\">20.&nbsp;In relation to&nbsp;a&nbsp;plane&nbsp;transmission grating&nbsp;with 5000&nbsp;lines&nbsp;per&nbsp;cm&nbsp;answer&nbsp;the&nbsp;<\/p>\n<p style=\"position:absolute;top:422px;left:189px;white-space:nowrap\" class=\"ft590\">following:&nbsp;<\/p>\n<p style=\"position:absolute;top:444px;left:162px;white-space:nowrap\" class=\"ft590\">21.&nbsp;&nbsp;&nbsp;&nbsp;For&nbsp;wavelength 6000A&nbsp;what is&nbsp;the&nbsp;highest order&nbsp;of spectrum&nbsp;which may&nbsp;be&nbsp;<\/p>\n<p style=\"position:absolute;top:466px;left:189px;white-space:nowrap\" class=\"ft590\">observed.&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:488px;left:162px;white-space:nowrap\" class=\"ft590\">22.&nbsp;&nbsp;If opaque&nbsp;spaces&nbsp;are&nbsp;exactly&nbsp;two&nbsp;times&nbsp;transparent spaces, which order&nbsp;of spectra&nbsp;<\/p>\n<p style=\"position:absolute;top:510px;left:189px;white-space:nowrap\" class=\"ft590\">will be&nbsp;absent?&nbsp;&nbsp;<\/p>\n<p style=\"position:absolute;top:532px;left:162px;white-space:nowrap\" class=\"ft590\">23.&nbsp;21&nbsp;Calculate&nbsp;the&nbsp;Brewster&rsquo;s&nbsp;angles&nbsp;for the&nbsp;following&nbsp;liquids&nbsp;Ethyl alcohols&nbsp;for which&nbsp;<\/p>\n<p style=\"position:absolute;top:554px;left:189px;white-space:nowrap\" class=\"ft590\">&micro;=1.361 and&nbsp;Carbon&nbsp;tetrachloride&nbsp;for&nbsp;which&nbsp;&micro;=1.461.&nbsp;<\/p>\n<p style=\"position:absolute;top:576px;left:162px;white-space:nowrap\" class=\"ft590\">24.&nbsp;22&nbsp;A&nbsp;glass plate&nbsp;is&nbsp;to&nbsp;be&nbsp;used&nbsp;as&nbsp;a polarizer.&nbsp;Find&nbsp;the&nbsp;angle&nbsp;of&nbsp;polarization&nbsp;for it&nbsp;.&nbsp;Also&nbsp;<\/p>\n<p style=\"position:absolute;top:598px;left:189px;white-space:nowrap\" class=\"ft590\">find angle&nbsp;of refraction.&nbsp;Give&nbsp;&micro; for&nbsp;glass&nbsp;1.54.&nbsp;<\/p>\n<p style=\"position:absolute;top:620px;left:162px;white-space:nowrap\" class=\"ft590\">25.&nbsp;23&nbsp;Calculate&nbsp;the&nbsp;thickness&nbsp;of a&nbsp;quarter&nbsp;wave&nbsp;plate&nbsp;made&nbsp;of quartz to&nbsp;be&nbsp;used with&nbsp;<\/p>\n<p style=\"position:absolute;top:642px;left:189px;white-space:nowrap\" class=\"ft590\">sodium&nbsp;light&nbsp;&lambda;=6000A&nbsp;&micro;o=1.544&nbsp;and&nbsp;&micro;e=1.533.&nbsp;<\/p>\n<p style=\"position:absolute;top:663px;left:162px;white-space:nowrap\" class=\"ft590\">26.&nbsp;24&nbsp;Determine&nbsp;the&nbsp;thickness&nbsp;of a&nbsp;crystal&nbsp;plate&nbsp;of calcite&nbsp;which can produce&nbsp;circular&nbsp;<\/p>\n<p style=\"position:absolute;top:686px;left:189px;white-space:nowrap\" class=\"ft590\">polarized&nbsp;light.&nbsp;For&nbsp;calcite&nbsp;&micro;e=&nbsp;1.486&nbsp;and&nbsp;&micro;o=1.658&nbsp;and&nbsp;&lambda;=5893A.&nbsp;<\/p>\n<p style=\"position:absolute;top:707px;left:162px;white-space:nowrap\" class=\"ft590\">27.&nbsp;25&nbsp;Calculate&nbsp;the&nbsp;minimum&nbsp;thickness&nbsp;of a&nbsp;plate&nbsp;if the&nbsp;ordinary&nbsp;and extra&nbsp;ordinary&nbsp;rays&nbsp;<\/p>\n<p style=\"position:absolute;top:729px;left:189px;white-space:nowrap\" class=\"ft590\">coming&nbsp;out&nbsp;mix&nbsp;up from&nbsp;plane&nbsp;polarized&nbsp;light&nbsp;given&nbsp;&lambda;=6000A&nbsp;&micro;o=1.562&nbsp;and&nbsp;<\/p>\n<p style=\"position:absolute;top:751px;left:189px;white-space:nowrap\" class=\"ft590\">&micro;e=1.552.&nbsp;<\/p>\n<p style=\"position:absolute;top:773px;left:108px;white-space:nowrap\" class=\"ft591\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:793px;left:108px;white-space:nowrap\" class=\"ft591\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:814px;left:108px;white-space:nowrap\" class=\"ft591\"><b>&nbsp;<\/b><\/p>\n<p style=\"position:absolute;top:856px;left:108px;white-space:nowrap\" class=\"ft590\">&nbsp;<\/p>\n<p style=\"position:absolute;top:899px;left:108px;white-space:nowrap\" class=\"ft590\">&nbsp;<\/p>\n<p style=\"position:absolute;top:941px;left:108px;white-space:nowrap\" class=\"ft590\">&nbsp;<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>1&nbsp; &nbsp; UNIT&nbsp;&ndash;&nbsp;2&nbsp; &nbsp; WAVE&nbsp;OPTICS&nbsp;&nbsp; Unit-02\/Lecture-01&nbsp; &nbsp; FRESNEL&nbsp;BIPRISM:-&nbsp; Fresnel&rsquo;s&nbsp;biprism is&nbsp;made&nbsp;by&nbsp;joining&nbsp;two&nbsp;thin&nbsp;prisms&nbsp;at&nbsp;their base&nbsp;to&nbsp;create&nbsp;a&nbsp;single&nbsp; triangular shape.&nbsp;Light&nbsp;from single&nbsp;slit&nbsp;S forms&nbsp;spherical waves&nbsp;incident&nbsp;on&nbsp;the&nbsp;biprism.&nbsp; Light passing&nbsp;through the&nbsp;lower&nbsp;section is&nbsp;refracted up, while&nbsp;light going&nbsp;into&nbsp;the&nbsp;top&nbsp; section is&nbsp;refracted down, forming&nbsp;a&nbsp;region where&nbsp;the&nbsp;beams&nbsp;interfere.&nbsp;This&nbsp;creates&nbsp;two&nbsp; virtual sources&nbsp;&nbsp;S 1 &nbsp;&nbsp;and S 2 ,&nbsp;with&nbsp;an&nbsp;apparent&nbsp;separation&nbsp;a.&nbsp;A biprism&nbsp;is&nbsp;essentially&nbsp;two&nbsp; prisms,&nbsp;each&nbsp;of&nbsp;very&nbsp;small refractive&nbsp;angle&nbsp;&alpha;&nbsp;placed&nbsp;base&nbsp;to&nbsp;base.&nbsp;In&nbsp;reality&nbsp;the&nbsp;biprism is&nbsp; constructed&nbsp;from&nbsp;a&nbsp;single&nbsp;plate&nbsp;of glass&nbsp;by&nbsp;suitable&nbsp;grinding&nbsp;and polishing&nbsp;it;&nbsp;the&nbsp;obtuse&nbsp; angle&nbsp;of the&nbsp;prism&nbsp;is&nbsp;only&nbsp;slightly&nbsp;less&nbsp;than 180&deg;&nbsp;and the&nbsp;other&nbsp;angles&nbsp;is&nbsp;of the&nbsp;order&nbsp;of&nbsp;30&rsquo;&nbsp; are&nbsp;equal.&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &#8230; <a title=\"Wave Optics From RGPV Engineering Physics Notes\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/wave-optics-from-rgpv-engineering-physics-notes\/\" aria-label=\"More on Wave Optics From RGPV Engineering Physics Notes\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2924],"tags":[],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/227060"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=227060"}],"version-history":[{"count":1,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/227060\/revisions"}],"predecessor-version":[{"id":227061,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/227060\/revisions\/227061"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=227060"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=227060"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=227060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}